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• Guide to Experimental Design | Overview, Steps, & Examples

Guide to Experimental Design | Overview, 5 steps & Examples

Published on December 3, 2019 by Rebecca Bevans . Revised on June 21, 2023.

Experiments are used to study causal relationships . You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design create a set of procedures to systematically test a hypothesis . A good experimental design requires a strong understanding of the system you are studying.

There are five key steps in designing an experiment:

• Consider your variables and how they are related
• Write a specific, testable hypothesis
• Design experimental treatments to manipulate your independent variable
• Assign subjects to groups, either between-subjects or within-subjects
• Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any  extraneous variables that might influence your results. If random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead. This minimizes several types of research bias, particularly sampling bias , survivorship bias , and attrition bias as time passes.

Table of contents

Step 1: define your variables, step 2: write your hypothesis, step 3: design your experimental treatments, step 4: assign your subjects to treatment groups, step 5: measure your dependent variable, other interesting articles, frequently asked questions about experiments.

You should begin with a specific research question . We will work with two research question examples, one from health sciences and one from ecology:

To translate your research question into an experimental hypothesis, you need to define the main variables and make predictions about how they are related.

Start by simply listing the independent and dependent variables .

Then you need to think about possible extraneous and confounding variables and consider how you might control  them in your experiment.

Finally, you can put these variables together into a diagram. Use arrows to show the possible relationships between variables and include signs to show the expected direction of the relationships.

Here we predict that increasing temperature will increase soil respiration and decrease soil moisture, while decreasing soil moisture will lead to decreased soil respiration.

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Now that you have a strong conceptual understanding of the system you are studying, you should be able to write a specific, testable hypothesis that addresses your research question.

The next steps will describe how to design a controlled experiment . In a controlled experiment, you must be able to:

• Systematically and precisely manipulate the independent variable(s).
• Precisely measure the dependent variable(s).
• Control any potential confounding variables.

If your study system doesn’t match these criteria, there are other types of research you can use to answer your research question.

How you manipulate the independent variable can affect the experiment’s external validity – that is, the extent to which the results can be generalized and applied to the broader world.

First, you may need to decide how widely to vary your independent variable.

• just slightly above the natural range for your study region.
• over a wider range of temperatures to mimic future warming.
• over an extreme range that is beyond any possible natural variation.

Second, you may need to choose how finely to vary your independent variable. Sometimes this choice is made for you by your experimental system, but often you will need to decide, and this will affect how much you can infer from your results.

• a categorical variable : either as binary (yes/no) or as levels of a factor (no phone use, low phone use, high phone use).
• a continuous variable (minutes of phone use measured every night).

How you apply your experimental treatments to your test subjects is crucial for obtaining valid and reliable results.

First, you need to consider the study size : how many individuals will be included in the experiment? In general, the more subjects you include, the greater your experiment’s statistical power , which determines how much confidence you can have in your results.

Then you need to randomly assign your subjects to treatment groups . Each group receives a different level of the treatment (e.g. no phone use, low phone use, high phone use).

You should also include a control group , which receives no treatment. The control group tells us what would have happened to your test subjects without any experimental intervention.

When assigning your subjects to groups, there are two main choices you need to make:

• A completely randomized design vs a randomized block design .
• A between-subjects design vs a within-subjects design .

Randomization

An experiment can be completely randomized or randomized within blocks (aka strata):

• In a completely randomized design , every subject is assigned to a treatment group at random.
• In a randomized block design (aka stratified random design), subjects are first grouped according to a characteristic they share, and then randomly assigned to treatments within those groups.

Sometimes randomization isn’t practical or ethical , so researchers create partially-random or even non-random designs. An experimental design where treatments aren’t randomly assigned is called a quasi-experimental design .

Between-subjects vs. within-subjects

In a between-subjects design (also known as an independent measures design or classic ANOVA design), individuals receive only one of the possible levels of an experimental treatment.

In medical or social research, you might also use matched pairs within your between-subjects design to make sure that each treatment group contains the same variety of test subjects in the same proportions.

In a within-subjects design (also known as a repeated measures design), every individual receives each of the experimental treatments consecutively, and their responses to each treatment are measured.

Within-subjects or repeated measures can also refer to an experimental design where an effect emerges over time, and individual responses are measured over time in order to measure this effect as it emerges.

Counterbalancing (randomizing or reversing the order of treatments among subjects) is often used in within-subjects designs to ensure that the order of treatment application doesn’t influence the results of the experiment.

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Finally, you need to decide how you’ll collect data on your dependent variable outcomes. You should aim for reliable and valid measurements that minimize research bias or error.

Some variables, like temperature, can be objectively measured with scientific instruments. Others may need to be operationalized to turn them into measurable observations.

• Ask participants to record what time they go to sleep and get up each day.
• Ask participants to wear a sleep tracker.

How precisely you measure your dependent variable also affects the kinds of statistical analysis you can use on your data.

Experiments are always context-dependent, and a good experimental design will take into account all of the unique considerations of your study system to produce information that is both valid and relevant to your research question.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic

Experimental design means planning a set of procedures to investigate a relationship between variables . To design a controlled experiment, you need:

• A testable hypothesis
• At least one independent variable that can be precisely manipulated
• At least one dependent variable that can be precisely measured

When designing the experiment, you decide:

• How you will manipulate the variable(s)
• How you will control for any potential confounding variables
• How many subjects or samples will be included in the study
• How subjects will be assigned to treatment levels

Experimental design is essential to the internal and external validity of your experiment.

The key difference between observational studies and experimental designs is that a well-done observational study does not influence the responses of participants, while experiments do have some sort of treatment condition applied to at least some participants by random assignment .

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word “between” means that you’re comparing different conditions between groups, while the word “within” means you’re comparing different conditions within the same group.

An experimental group, also known as a treatment group, receives the treatment whose effect researchers wish to study, whereas a control group does not. They should be identical in all other ways.

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Design of Experiments (DOE): A Comprehensive Overview on Its Meaning and Usage

The methodological framework known as Design of Experiments (DOE) is transformative in various disciplines, allowing researchers and practitioners the ability to plan, conduct, analyze, and interpret controlled tests to evaluate the factors that may influence a particular outcome. Historically grounded in agricultural and scientific research, DOE has burgeoned into an indispensable tool across a myriad of industries, including manufacturing, healthcare, and marketing. This article aims to elucidate the concepts and applications of Design of Experiments, providing a panoramic as well as an in-depth view of its various principles, types, statistical underpinnings, and practical applications.

Introduction to Design of Experiments (DOE)

Definition and basics of design of experiments.

Design of Experiments, at its core, is a structured methodological approach used to determine the relationship between factors affecting a process and the output of that process. It encompasses a vast array of strategies for testing hypotheses concerning the factors that could influence a particular variable of interest. The primary aim is not only to affirm the effect of these factors but also to quantify the extent to which they influence results, thus providing a scientific basis for decision-making.

Importance and relevance of DOE

In the contemporary landscape of problem-solving, the significance of DOE is multifaceted. It facilitates a systematic approach to experimentation that is both efficient and economical, reducing the number of trials needed to gather meaningful data. For instance, industries seeking to enhance their product quality can rely on DOE to guide them in identifying significant variables and their optimal settings. Moreover, DOE is an integral component of an effective problem solving techniques course or online certificate courses , as it equips students and professionals with the analytical skills necessary to tackle complex challenges.

Brief history and development of DOE

The foundations of Design of Experiments can be traced back to the early 20th century with the pioneering work of Ronald A. Fisher in the realm of agricultural research. His seminal contributions laid the groundwork for modern DOE, particularly in the context of controlling variation and maximizing information gain. As statistical methods have evolved, DOE has continued to grow in sophistication, integrating advances in computation and information technology to broaden its applicability across various fields.

Key Principles of Design of Experiments (DOE)

Randomization, what is randomization in doe.

Randomization is the backbone of a rigorous experimental design as it mitigates the effects of uncontrolled variables, or confounding factors, ensuring that the treatment groups are comparable. By assigning experimental units to treatment conditions randomly, researchers can confidently attribute differences in outcomes to the factors under study rather than to extraneous variables.

Benefits and significance of randomization

The paramount importance of randomization lies in its capacity to elevate the internal validity of an experiment. It reduces bias and ensures an unbiased estimate of the treatment effect, thus bolstering the credibility of the experimental results. This key principle is an assurance that the experiment's findings can be generalized beyond the study parameters.

Examples illustrating randomization

Consider a clinical trial for a new pharmaceutical product. If participants are randomized into the control and treatment groups, any difference observed in outcomes can be attributed to the drug's effectiveness rather than patient characteristics. This methodological rigor is what makes randomization indispensable in DOE.

Replication

Understanding replication in the context of doe.

Replication is the repeated application of certain conditions within an experiment to ensure that results are not anomalies. It adds precision to the experiment by allowing variance estimation, which is crucial for assessing the reliability of the findings.

Its role and importance in DOE

The role of replication in DOE cannot be overstressed. It affords the experimenter the ability to discern true effects from random errors, thus confirming the consistency of experimental results. When used judiciously, replication improves the power of the experiment, enabling more definitive conclusions.

Applicable examples of replication

For instance, verifying the strength of a newly engineered material could involve subjecting multiple samples to stress tests under identical conditions. The consistency in the failure threshold across these samples would indicate the reliability of the material's design as determined through replication.

Concept of blocking in DOE

Blocking is a technique used to account for variability among experimental units that cannot be eliminated. By grouping similar experimental units together and carrying out the same experimental conditions within these blocks, one can control the variables leading to variability within each group, thus reducing overall experimental error.

Advantages of using blocking in DOE

Employing blocking in an experiment minimizes the confounding effects of variables that are known but not directly of interest to the study. This approach increases the precision of the estimates of main effects and interactions by isolating the block-to-block variability from the treatment effects. It is particularly useful when one wants to account for heterogeneity among subjects or any other nuisance variable.

Real-world blocking examples

In an agricultural study, fields could be blocked by soil type before the application of different fertilization regimes. This ensures that variation due to soil composition does not skew the results, thus giving a clearer understanding of the fertilizers' effectiveness.

Categories of Design of Experiments (DOE)

Full-factorial design, overview and basic understanding.

Full-factorial design involves the investigation of every possible combination of factors and their levels. Each treatment combination is applied to separate units in an experiment, making it a comprehensive approach that allows for the assessment of both main effects and interactions between factors.

Strengths and limitations

While the full-factorial design provides a wealth of information about the factors in question, it can be resource-intensive and impractical when dealing with a large number of factors. However, if resources allow, this type of design delivers the most exhaustive data on the effects and possible interactions.

Use case example of full-factorial design

A manufacturer could use a full-factorial design to understand the impact of temperature and pressure on the strength of a welded joint. By varying these factors systematically across all levels, the manufacturer could determine the optimal conditions for the welding process that ensure joint strength.

Fractional-factorial Design

Definition and understanding of the concept.

Fractional-factorial design is an efficient variation of the full-factorial design that investigates only a subset of the possible combinations of factor levels. By strategically selecting a fraction of the full design, researchers can still gather information on the most crucial factors influencing an outcome while significantly reducing the number of experiments.

Advantages and drawbacks

This design's main advantage is its economy in terms of time and resources. Nonetheless, this comes with the potential drawback of confounding, which is when two or more factor effects cannot be separated due to the design's reduced size. Researchers must balance the need for information with the constraints of their experimental budget.

Case study demonstrating the use of fractional-factorial design

A tech company wanting to assess the design features impacting user engagement might employ a fractional-factorial design to investigate a manageable subset of combinations rather than exhaust every potential variation, thereby identifying critical design elements efficiently.

Response Surface Design

Explaining response surface design.

Response Surface Design (RSD) is focused on modeling the relationship between a response and a set of quantitative variables. It is particularly useful when the goal is optimization, as RSD can identify the levels of factors that lead to the best possible outcome.

Pros and cons of using Response Surface Design

RSD exhibits potency in exploring complex, nonlinear relationships and can be pivotal in honing in on optimal conditions. However, constructing a suitable response surface model often requires a more significant number of experimental runs compared to simpler designs, and interpreting the resulting model may necessitate a substantial level of statistical expertise.

Applicable example of response surface design

An example might involve a food scientist employing RSD to optimize a recipe for flavor and texture by manipulating ingredient ratios and cooking times. By analyzing the response surface, the scientist can pinpoint the exact conditions that yield the best culinary result.

Statistical Analysis in Design of Experiments (DOE)

Role of statistical analysis in doe.

Statistical analysis is fundamental in DOE, as it transforms experimental data into meaningful insights. Here, analytic techniques are employed to discern patterns, test hypotheses, and derive conclusions that can withstand scrutiny within the scientific community.

Various statistical techniques applied in DOE

The array of statistical methods applied within DOE is expansive, encompassing t-tests, ANOVA, regression analysis, and multivariate techniques, among others. Selecting the appropriate method hinges on the complexity of the data structure and the goals of the research.

Examples demonstrating the importance of statistical analysis in DOE

For instance, a multinational corporation might conduct a series of experiments to improve a product feature. Utilizing ANOVA, researchers can determine whether differences in quality metrics across various production sites are statistically significant, guiding quality improvement efforts.

Practical Applications of Design of Experiments (DOE)

Doe in product and process development.

DOE plays a critical role in new product development and process refinement. By assessing the impact of variable changes, designers and engineers can develop superior products and streamline processes for improved performance and cost-efficiency.

The role of DOE in industrial manufacturing

In the context of industrial manufacturing, DOE is an invaluable asset. It assists in identifying key process factors and optimizing manufacturing conditions, resulting in enhanced quality control and reduced production costs—a boon for competitiveness in the market.

Case studies showing the impact of DOE in various fields

Case studies from the pharmaceutical industry to aerospace engineering demonstrate DOE's vital contributions. Whether optimizing drug formulations or adjusting flight parameters, DOE's applications are incredibly diverse and contribute significantly to scientific and technological advancements.

Conclusion: Future Trends and Developments in Design of Experiments (DOE)

Current trends in doe.

The recent trends in DOE point towards the integration of more advanced computational techniques, like machine learning algorithms, to handle complex, high-dimensional data sets and to refine predictive models for experimental outcomes.

Future outlook and potential advancements in DOE

Looking ahead, we may witness the further development of real-time analytics in DOE, enabling even more dynamic exploration of experiment spaces, perhaps leading to adaptive experimentation that could revolutionize fields as disparate as genomics and supply chain management.

Final thoughts and recommendations for further studies in DOE

As the landscape of DOE progresses, so does the need for educational pursuits such as online certificate courses in this area, fostering a new generation of adept experimenters equipped with equipped with the latest tools and techniques. Investigators are encouraged to undertake further studies in DOE to harness its full potential—a testament to the enduring relevance and flexibility of this methodological powerhouse.

What are the key characteristics of a well-designed experiment in research methodology?

Well-designed experiment essentials, clarity in purpose.

A well-crafted experiment begins with a crystal-clear objective. Researchers should articulate their primary questions. These drive the experiment. Specific goals guide the study's structure. Precise objectives leave no room for ambiguity. Clear aims ensure focused data collection. This results in robust and relevant findings. Clarity underscores every experiment layer.

Rigorous Planning

Rigorous planning underpins scientific integrity. Researchers craft detailed protocols. These serve as experiments' blueprints. They outline every step and contingency. Careful design minimizes unwanted variables' intrusion. It ensures the experiment can test hypotheses effectively. Predefined procedures guarantee the study's repeatability. Other scientists can replicate the study with ease.

Controlled Conditions

Experiments thrive under control. Researchers strive for controlled environments. They manage variables meticulously. Control is not absolute but optimized. Key is distinguishing between independent and dependent variables. Independent variables undergo deliberate changes. Researchers measure dependent variables for effect assessments. Control groups provide a comparison benchmark. They remain untouched, isolating the independent variable’s impact.

Randomization and Blinding

Randomization promotes objectivity. It mitigates selection bias. Participants or samples receive random allocation. This ensures equal distribution of confounding variables. Blind or double-blind setups conceal information. Subjects or researchers remain unaware of certain details. This prevents bias from influencing outcomes. Blinding strengthens an experiment's credibility.

Sufficient Sample Size

Sample size holds crucial importance. It must be statistically sufficient. Adequacy enables valid generalizations. Small samples undermine the study's validity. They invite chance-driven anomalies. Optimal size depends on the expected effect size. Power analysis often determines the required sample. Researchers seek a balance. Overly large samples waste resources. Insufficient samples yield inconclusive results.

Ethical Considerations

Ethical concerns stand paramount. Researchers uphold rigorous ethical standards. Participants give informed consent. They understand the experiment's nature. Ethical treatment extends beyond humans. Animal studies require humane conduct. Ethical oversight comes from institutional review boards. They assess risks versus benefits. They ensure research integrity.

Data Analysis Plan

Planning extends to data analysis. Researchers must decide on this before data collection. They determine which statistical tests fit their data. They predefine significance levels. This minimizes data dredging after the fact. A thorough plan prevents misleading analytic practices. It directs researchers to honest interpretations.

Transparent Reporting

Finally, clarity in reporting is essential. Researchers describe their methods in detail. They disclose all conditions, variables, and results. Transparency fosters trust in the findings. It enables other scientists to verify results. Clear reporting is the capstone of a well-designed experiment.

In summary, these characteristics thread through exemplary research. They elevate experiments from mere inquiry to scientific evidence. They bolster confidence in the knowledge we gain. Researchers must adhere to these tenets. Only then can we rely on their discoveries.

How does Design of Experiments contribute towards the efficacy and efficiency of a study?

Unveiling the power of design of experiments, efficient resource utilization.

Design of Experiments (DoE) stands pivotal. It optimizes resource allocation. Fewer resources yield comprehensive data. This translates into significant cost savings. Each experiment harnesses maximal information gain.

Enhanced Understanding

DoE allows for a better grasp of variables. It clarifies the interaction between factors. Such insights foster informed decision-making. They also streamline the research process considerably.

Systematic Approach

The approach of DoE is inevitably systematic. It eliminates the hit-and-miss experiments. Every trial becomes a well-thought-out step. Researchers work with clear objectives and methods.

Reduction of Experimental Runs

One key benefit is reduced experimental runs. DoE leverages factorial designs. These designs assess multiple factors simultaneously. They aid in understanding complex interactions swiftly. Thus, they reduce the number of required experiments.

Data Quality Improvement

With DoE, data quality improves. The method ensures a structured data collection. Bias minimization is a direct outcome. Consistent and high-quality data is the result. This robustness adds credibility to the study.

Accelerated Timeframes

DoE can significantly hasten experimentation. A thorough initial planning phase foresees potential obstacles. It also identifies the most critical factors early on. Time saved here quickens overall study completion.

Risk Mitigation

Risk reduction is another aspect. DoE helps in anticipating variability. Researchers understand possible outcomes better. Preemptive measures are then easier to implement.

Decision-Making Precision

DoE offers precise guidance for decision-making. It sorts critical from trivial factors. Decisions are therefore more data-driven. Their precision enhances the study's value.

Optimization of Conditions

It aids in the optimization of experimental conditions. Optimal settings are quickly identified. This leads to better product quality or process efficiency.

Design of Experiments revolutionizes research efficacy and efficiency. Researchers see DoE as more than a tool. It's a strategic ally in scientific inquiry. Its methodical, efficient, and data-centric approach is unmatched. The results? Enhanced understanding, quality, and breakthroughs in less time.

What are the potential pitfalls or challenges that researchers may encounter when using Design of Experiments and how can these be mitigated?

Understanding design of experiments.

Design of Experiments ( DoE ) serves as a powerful tool. It enables researchers to systematically explore complexities in various fields. In DoE, potential confounding factors can skew results. Researchers must handle these with care. Proper experimental design is thus pivotal.

Addressing Complex Interactions

Interactions among variables often complicate DoE. These interactions can mask true effects. Identify key factors before experimentation. Focus on a manageable number of interactions. Simplify the complexity of your study.

Adequate Sample Size and Replicability

Sample size directly affects the power of an experiment. Too small a size may miss vital nuances. Ensure the sample size supports your study's objective. Replicability is a cornerstone of scientific research. Repetition validates the initial findings. Plan duplicate runs to confirm results.

Controlling External Variability

Uncontrolled external factors introduce noise. This noise can reduce the clarity of findings. Maintain strict environmental control where possible. Strive for consistency across all experimental conditions.

Choosing the Right Design

Selecting an inappropriate design can lead to misleading conclusions. Understand the strengths and weaknesses of different designs. Tailor the design to your specific research question.

Handling Missing or Outlying Data

Data may go missing or fall outside expected ranges. Develop a plan for dealing with such data. Consider statistical methods like imputation for missing values. Apply outlier tests to determine the fate of anomalies.

Statistical Proficiency

DoE demands statistical knowledge. Interpret results with statistical confidence. Derive meaningful insights without overstepping the data's bounds. Stay educated on statistical methods relevant to DoE.

Ethical concerns must guide any experimental work. Ensure that your design minimizes potential harm. Adhere to ethical standards throughout your research.

Mitigating Challenges in DoE

Researchers can take steps to improve the robustness of their experimental designs.

- Plan Thoroughly : Pre-experimental planning is critical. Anticipate challenges and lay out a clear roadmap.

- Pilot Studies : Conduct preliminary tests. These can highlight unforeseen issues. Address these before proceeding with the full-scale experiment.

- Educate Yourself : Nurture a deep understanding of DoE principles. Attend workshops and seminars. Stay abreast of advancements in experimental design.

- Consult Experts : Do not hesitate to seek advice. Collaborate with statisticians and experts. Their insights can help craft a more sound experiment.

- Software Tools : Leverage software designed for DoE. These can automate complex statistical computations. Ensure accuracy in your design and analysis.

- Documentation : Keep detailed records of every step. Document the rationale behind decisions. This transparency aids in replicating and validating results.

Engagement with these strategies can lead to stronger, more reliable experiments. It enables researchers to maneuver through potential pitfalls confidently. Acknowledge the complexities of DoE. Strive for rigor in design and execution. The reward is valid, reproducible knowledge that advances your field.

He is a content producer who specializes in blog content. He has a master's degree in business administration and he lives in the Netherlands.

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Experimental Design: Definition and Types

By Jim Frost 3 Comments

What is Experimental Design?

An experimental design is a detailed plan for collecting and using data to identify causal relationships. Through careful planning, the design of experiments allows your data collection efforts to have a reasonable chance of detecting effects and testing hypotheses that answer your research questions.

An experiment is a data collection procedure that occurs in controlled conditions to identify and understand causal relationships between variables. Researchers can use many potential designs. The ultimate choice depends on their research question, resources, goals, and constraints. In some fields of study, researchers refer to experimental design as the design of experiments (DOE). Both terms are synonymous.

Ultimately, the design of experiments helps ensure that your procedures and data will evaluate your research question effectively. Without an experimental design, you might waste your efforts in a process that, for many potential reasons, can’t answer your research question. In short, it helps you trust your results.

Learn more about Independent and Dependent Variables .

Design of Experiments: Goals & Settings

Experiments occur in many settings, ranging from psychology, social sciences, medicine, physics, engineering, and industrial and service sectors. Typically, experimental goals are to discover a previously unknown effect , confirm a known effect, or test a hypothesis.

Effects represent causal relationships between variables. For example, in a medical experiment, does the new medicine cause an improvement in health outcomes? If so, the medicine has a causal effect on the outcome.

An experimental design’s focus depends on the subject area and can include the following goals:

• Understanding the relationships between variables.
• Identifying the variables that have the largest impact on the outcomes.
• Finding the input variable settings that produce an optimal result.

For example, psychologists have conducted experiments to understand how conformity affects decision-making. Sociologists have performed experiments to determine whether ethnicity affects the public reaction to staged bike thefts. These experiments map out the causal relationships between variables, and their primary goal is to understand the role of various factors.

Conversely, in a manufacturing environment, the researchers might use an experimental design to find the factors that most effectively improve their product’s strength, identify the optimal manufacturing settings, and do all that while accounting for various constraints. In short, a manufacturer’s goal is often to use experiments to improve their products cost-effectively.

In a medical experiment, the goal might be to quantify the medicine’s effect and find the optimum dosage.

Developing an Experimental Design

Developing an experimental design involves planning that maximizes the potential to collect data that is both trustworthy and able to detect causal relationships. Specifically, these studies aim to see effects when they exist in the population the researchers are studying, preferentially favor causal effects, isolate each factor’s true effect from potential confounders, and produce conclusions that you can generalize to the real world.

To accomplish these goals, experimental designs carefully manage data validity and reliability , and internal and external experimental validity. When your experiment is valid and reliable, you can expect your procedures and data to produce trustworthy results.

An excellent experimental design involves the following:

• Lots of preplanning.
• Developing experimental treatments.
• Determining how to assign subjects to treatment groups.

The remainder of this article focuses on how experimental designs incorporate these essential items to accomplish their research goals.

Learn more about Data Reliability vs. Validity and Internal and External Experimental Validity .

Preplanning, Defining, and Operationalizing for Design of Experiments

This phase of the design of experiments helps you identify critical variables, know how to measure them while ensuring reliability and validity, and understand the relationships between them. The review can also help you find ways to reduce sources of variability, which increases your ability to detect treatment effects. Notably, the literature review allows you to learn how similar studies designed their experiments and the challenges they faced.

Operationalizing a study involves taking your research question, using the background information you gathered, and formulating an actionable plan.

This process should produce a specific and testable hypothesis using data that you can reasonably collect given the resources available to the experiment.

• Null hypothesis : The jumping exercise intervention does not affect bone density.
• Alternative hypothesis : The jumping exercise intervention affects bone density.

To learn more about this early phase, read Five Steps for Conducting Scientific Studies with Statistical Analyses .

Formulating Treatments in Experimental Designs

In an experimental design, treatments are variables that the researchers control. They are the primary independent variables of interest. Researchers administer the treatment to the subjects or items in the experiment and want to know whether it causes changes in the outcome.

As the name implies, a treatment can be medical in nature, such as a new medicine or vaccine. But it’s a general term that applies to other things such as training programs, manufacturing settings, teaching methods, and types of fertilizers. I helped run an experiment where the treatment was a jumping exercise intervention that we hoped would increase bone density. All these treatment examples are things that potentially influence a measurable outcome.

Even when you know your treatment generally, you must carefully consider the amount. How large of a dose? If you’re comparing three different temperatures in a manufacturing process, how far apart are they? For my bone mineral density study, we had to determine how frequently the exercise sessions would occur and how long each lasted.

How you define the treatments in the design of experiments can affect your findings and the generalizability of your results.

Assigning Subjects to Experimental Groups

A crucial decision for all experimental designs is determining how researchers assign subjects to the experimental conditions—the treatment and control groups. The control group is often, but not always, the lack of a treatment. It serves as a basis for comparison by showing outcomes for subjects who don’t receive a treatment. Learn more about Control Groups .

How your experimental design assigns subjects to the groups affects how confident you can be that the findings represent true causal effects rather than mere correlation caused by confounders. Indeed, the assignment method influences how you control for confounding variables. This is the difference between correlation and causation .

Imagine a study finds that vitamin consumption correlates with better health outcomes. As a researcher, you want to be able to say that vitamin consumption causes the improvements. However, with the wrong experimental design, you might only be able to say there is an association. A confounder, and not the vitamins, might actually cause the health benefits.

Let’s explore some of the ways to assign subjects in design of experiments.

Completely Randomized Designs

A completely randomized experimental design randomly assigns all subjects to the treatment and control groups. You simply take each participant and use a random process to determine their group assignment. You can flip coins, roll a die, or use a computer. Randomized experiments must be prospective studies because they need to be able to control group assignment.

Random assignment in the design of experiments helps ensure that the groups are roughly equivalent at the beginning of the study. This equivalence at the start increases your confidence that any differences you see at the end were caused by the treatments. The randomization tends to equalize confounders between the experimental groups and, thereby, cancels out their effects, leaving only the treatment effects.

For example, in a vitamin study, the researchers can randomly assign participants to either the control or vitamin group. Because the groups are approximately equal when the experiment starts, if the health outcomes are different at the end of the study, the researchers can be confident that the vitamins caused those improvements.

Statisticians consider randomized experimental designs to be the best for identifying causal relationships.

If you can’t randomly assign subjects but want to draw causal conclusions about an intervention, consider using a quasi-experimental design .

Learn more about Randomized Controlled Trials and Random Assignment in Experiments .

Randomized Block Designs

Nuisance factors are variables that can affect the outcome, but they are not the researcher’s primary interest. Unfortunately, they can hide or distort the treatment results. When experimenters know about specific nuisance factors, they can use a randomized block design to minimize their impact.

This experimental design takes subjects with a shared “nuisance” characteristic and groups them into blocks. The participants in each block are then randomly assigned to the experimental groups. This process allows the experiment to control for known nuisance factors.

Blocking in the design of experiments reduces the impact of nuisance factors on experimental error. The analysis assesses the effects of the treatment within each block, which removes the variability between blocks. The result is that blocked experimental designs can reduce the impact of nuisance variables, increasing the ability to detect treatment effects accurately.

Suppose you’re testing various teaching methods. Because grade level likely affects educational outcomes, you might use grade level as a blocking factor. To use a randomized block design for this scenario, divide the participants by grade level and then randomly assign the members of each grade level to the experimental groups.

A standard guideline for an experimental design is to “Block what you can, randomize what you cannot.” Use blocking for a few primary nuisance factors. Then use random assignment to distribute the unblocked nuisance factors equally between the experimental conditions.

You can also use covariates to control nuisance factors. Learn about Covariates: Definition and Uses .

Observational Studies

In some experimental designs, randomly assigning subjects to the experimental conditions is impossible or unethical. The researchers simply can’t assign participants to the experimental groups. However, they can observe them in their natural groupings, measure the essential variables, and look for correlations. These observational studies are also known as quasi-experimental designs. Retrospective studies must be observational in nature because they look back at past events.

Imagine you’re studying the effects of depression on an activity. Clearly, you can’t randomly assign participants to the depression and control groups. But you can observe participants with and without depression and see how their task performance differs.

Observational studies let you perform research when you can’t control the treatment. However, quasi-experimental designs increase the problem of confounding variables. For this design of experiments, correlation does not necessarily imply causation. While special procedures can help control confounders in an observational study, you’re ultimately less confident that the results represent causal findings.

Learn more about Observational Studies .

For a good comparison, learn about the differences and tradeoffs between Observational Studies and Randomized Experiments .

Between-Subjects vs. Within-Subjects Experimental Designs

When you think of the design of experiments, you probably picture a treatment and control group. Researchers assign participants to only one of these groups, so each group contains entirely different subjects than the other groups. Analysts compare the groups at the end of the experiment. Statisticians refer to this method as a between-subjects, or independent measures, experimental design.

In a between-subjects design , you can have more than one treatment group, but each subject is exposed to only one condition, the control group or one of the treatment groups.

A potential downside to this approach is that differences between groups at the beginning can affect the results at the end. As you’ve read earlier, random assignment can reduce those differences, but it is imperfect. There will always be some variability between the groups.

In a  within-subjects experimental design , also known as repeated measures, subjects experience all treatment conditions and are measured for each. Each subject acts as their own control, which reduces variability and increases the statistical power to detect effects.

In this experimental design, you minimize pre-existing differences between the experimental conditions because they all contain the same subjects. However, the order of treatments can affect the results. Beware of practice and fatigue effects. Learn more about Repeated Measures Designs .

Design of Experiments Examples

For example, a bone density study has three experimental groups—a control group, a stretching exercise group, and a jumping exercise group.

In a between-subjects experimental design, scientists randomly assign each participant to one of the three groups.

In a within-subjects design, all subjects experience the three conditions sequentially while the researchers measure bone density repeatedly. The procedure can switch the order of treatments for the participants to help reduce order effects.

Matched Pairs Experimental Design

A matched pairs experimental design is a between-subjects study that uses pairs of similar subjects. Researchers use this approach to reduce pre-existing differences between experimental groups. It’s yet another design of experiments method for reducing sources of variability.

Researchers identify variables likely to affect the outcome, such as demographics. When they pick a subject with a set of characteristics, they try to locate another participant with similar attributes to create a matched pair. Scientists randomly assign one member of a pair to the treatment group and the other to the control group.

On the plus side, this process creates two similar groups, and it doesn’t create treatment order effects. While matched pairs do not produce the perfectly matched groups of a within-subjects design (which uses the same subjects in all conditions), it aims to reduce variability between groups relative to a between-subjects study.

On the downside, finding matched pairs is very time-consuming. Additionally, if one member of a matched pair drops out, the other subject must leave the study too.

Learn more about Matched Pairs Design: Uses & Examples .

Another consideration is whether you’ll use a cross-sectional design (one point in time) or use a longitudinal study to track changes over time .

A case study is a research method that often serves as a precursor to a more rigorous experimental design by identifying research questions, variables, and hypotheses to test. Learn more about What is a Case Study? Definition & Examples .

In conclusion, the design of experiments is extremely sensitive to subject area concerns and the time and resources available to the researchers. Developing a suitable experimental design requires balancing a multitude of considerations. A successful design is necessary to obtain trustworthy answers to your research question and to have a reasonable chance of detecting treatment effects when they exist.

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March 23, 2024 at 2:35 pm

Dear Jim You wrote a superb document, I will use it in my Buistatistics course, along with your three books. Thank you very much! Miguel

March 23, 2024 at 5:43 pm

Thanks so much, Miguel! Glad this post was helpful and I trust the books will be as well.

April 10, 2023 at 4:36 am

What are the purpose and uses of experimental research design?

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Design of Experiments: Definition, How It Works, & Examples

In the world of research, development, and innovation, making informed decisions based on reliable data is crucial. This is where the Design of Experiments (DoE) methodology steps in. DoE provides a structured framework for designing experiments that efficiently identify the factors influencing a process, product, or system.

DoE provides a strong tool to help you accomplish your objectives, whether you work in software development, manufacturing, pharmaceuticals, or any other industry that needs optimization.

This article by SkillTrans will analyze for you a better understanding of DoE through many different contents, including:

What is Design Of Experiments

Design Of Experiments Examples

Design Of Experiments Software

What Is Doe In Problem Solving

And What Is Doe In Testing

First of all, let's learn the definition of DoE.

What is Design of Experiments?

According to Wikipedia , DoE is defined as follows: 

“The design of experiments (DOE or DOX), also known as experiment design or experimental design, is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation.”

To put it more simply, Design of Experiments (DoE) is a powerful statistical methodology that revolutionizes the way we conduct experiments and gain insights. At its core, DoE is a systematic and efficient approach to experimentation, allowing researchers, engineers, and scientists to study the relationship between multiple input variables (factors) and key output variables (responses).

Why DoE is Superior to Traditional Testing

Traditional testing methods often rely on a "one-factor-at-a-time" (OFAT) approach, where only one factor is changed while holding others constant. 

This method has several limitations:

Time-Consuming: Testing each factor individually can be incredibly slow, especially when dealing with numerous variables.

Misses Interactions: OFAT fails to capture how factors might interact with each other, leading to incomplete or even misleading results.

Inefficient: It often requires a large number of experiments to gain a comprehensive understanding of a system.

How DoE Works

DoE takes a different approach by carefully planning experiments where multiple factors are varied simultaneously according to a predetermined design. This allows for the investigation of both the individual effects of each factor (main effects) and the combined effects of multiple factors (interaction effects) . 

By doing so, DoE provides a more holistic and accurate picture of the system being studied.

Statistical Power of DoE

DoE uses statistical analysis to interpret experiment outcomes. DoE can quantify the impact of the major factors influencing the response, identify the best settings or conditions, and identify the components that influence the response by using a variety of statistical models.

Benefits of DoE

Reduced Costs: DoE often requires fewer experimental runs than OFAT, saving time and resources.

Improved Understanding: DoE provides a deeper understanding of complex systems by uncovering interactions between factors.

Robust Solutions: DoE helps identify solutions that are more robust to variations in factors, leading to greater reliability.

Faster Optimization: By simultaneously exploring a wider range of conditions, DoE can accelerate the optimization process.

Applications for DoE can be found in many different areas, such as software development, marketing, manufacturing, medicines, and agriculture. It is a priceless tool for innovation and advancement in a variety of sectors due to its capacity to quickly and effectively address complicated difficulties.

We will learn more about the areas where DoE is commonly used in the next section.

Design of Experiments Examples

DoE has a proven track record of solving complex problems and driving innovation across a wide range of sectors. Here are some examples:

Design of Experiments Examples in Manufacturing

DoE is used to optimize manufacturing processes like casting, molding, machining, and assembly . It helps identify optimal settings for temperature, pressure, cycle time, and other variables, leading to improved quality, reduced scrap, and lower costs.

Design of Experiments Examples in Pharmaceuticals

DoE plays a crucial role in drug development, helping to determine optimal dosages, identify the most effective combinations of ingredients, and optimize manufacturing processes for quality and consistency.

Design of Experiments Examples in Agriculture

DoE is widely used in agriculture to optimize crop yields, improve soil fertility, and develop more sustainable farming practices. It helps researchers understand the complex interactions between environmental factors, plant genetics, and farming techniques.

Design of Experiments Examples in Software Development

DoE is applied in software testing to optimize test coverage, prioritize test cases, and identify software vulnerabilities. It also helps developers understand how different code changes impact performance and reliability.

Design of Experiments Examples in Marketing

DoE is utilized in marketing to optimize pricing strategies, advertising campaigns, and product launches. It helps marketers understand how different factors influence consumer behavior, allowing them to tailor their strategies for maximum impact.

These examples are just a glimpse into the vast potential of DoE. To better understand DoE's contribution to different fields, let's take a look at DoE in more detail.

Design of Experiments Software

While the principles of DoE are rooted in statistics and experimental design, the emergence of sophisticated software tools has democratized the methodology, making it accessible to a wider audience. These tools simplify the entire DoE workflow , from initial planning to final analysis, empowering users to design, execute, and interpret experiments with confidence.

Key Features and Benefits of DoE Software

Experiment design.

DoE software helps users choose the best experimental design depending on their objectives, considerations, and available resources. It facilitates the creation of effective experimental plans, randomization of runs, and design matrices.

Statistical Modeling

The statistical models that explain the connection between variables and responses are automatically created by the software. Response surface models, analysis of variance ( ANOVA ), and linear regression are among the models it can fit.

Data Analysis

DoE software offers strong analytical capabilities for data analysis , such as effect estimation, model diagnostics, and hypothesis testing. It assists users in locating important variables, estimating their influence, and choosing the best configurations.

Optimization

Optimization algorithms are a common feature of DoE software packages, which assist users in determining the combination of factor values that maximizes or minimizes a desired result.

Visualization

To assist users in efficiently interpreting and communicating their findings, DoE software provides a variety of visualization tools, including Pareto charts , interaction plots, and response surface plots.

Popular DoE Software Options

Here are a few well-known DoE software you might want to look into:

JMP is a feature-rich statistical software package with strong DoE capabilities that was developed by SAS. It provides a large selection of designs, sophisticated statistical modeling capabilities, and an intuitive user interface.

A well-liked statistics program with plenty of DoE tools and an intuitive user interface is Minitab . It provides a wide range of designs, simple analysis tools, and lucid visualizations.

Design-Expert

Specialized DoE software called Design-Expert concentrates on response surface methodology (RSM). It offers an easy-to-use interface for creating, evaluating, and refining complicated interaction experiments.

Stat-Ease 360

Stat-Ease 360 , a more comprehensive version of Design-Expert, interfaces with Python to enable custom scripting and sophisticated analysis.

Other Options

There are numerous other DoE software options available, each with its own strengths and target audience. Some examples include Cornerstone, MODDE, and Unscrambler .

The intricacy of the trials, financial limitations, features that are wanted, and the user's degree of statistical competence all influence the choice of DoE software. In order to provide consumers the opportunity to test out the features and functioning before deciding to buy, many software companies offer free trials.

DoE in Problem Solving

Identifying effective solutions and determining the underlying causes of complex problems can be challenging due to the presence of various interacting components. Design of Experiments (DoE) provides a methodical, data-driven approach to resolving these issues and making wise choices. 

Here's a closer look at the DoE problem-solving process :

Define the Problem with Metrics

The first step in using metrics and Design of Experiments to effectively address a problem is to precisely define the pertinent, quantifiable problem. For example, state the challenge as "reduce defect rate by 20% within six months" rather than aiming for something as abstract as "improve product quality." 

For the purpose of problem-solving, clearly define your aims and objectives and what you want to accomplish through experimenting. 

Furthermore, ascertain which important parties will be impacted by the issue and its resolution, and make sure that their requirements and viewpoints are taken into account at every stage of the process.

Identify Factors with Potential Impact

Start by thinking and making a list of every potential input variable that can have an impact on the result or response variable in order to uncover elements that could have an impact. These variables may include uncontrollable ones like raw material variability or ambient circumstances, as well as controllable ones like temperature, pressure, or ingredient proportions. 

After you have a complete list, rank the elements according to how they might affect the answer. You can determine the relative relevance of each item by utilizing previous information, professional judgment, or preliminary evidence. 

Furthermore, take into account how different elements interact with one another, as some may have an effect that is different from each of them alone.

Design the Experiment with Statistical Rigor

The first step in creating an experiment with statistical rigor is choosing an acceptable experimental design that takes into account the number of variables, the desired level of detail, and the resources that are available. Response surface designs, factorial designs, and fractional factorial designs are examples of common designs. 

Subsequently, ascertain the necessary number of experimental runs to attain statistically significant outcomes, taking into account variables like the intended confidence level, response variability, and the target effect size. 

In order to reduce the influence of uncontrollable circumstances and maximize the reliability and objectivity of the results, finally arrange the experimental runs in a random sequence.

Analyze the Results with Statistical Tools

In order to use statistical tools to analyze the outcomes, first gather data from the experiments and analyze it with applicable procedures like regression analysis, analysis of variance (ANOVA), or other pertinent statistical approaches. 

Determine which statistically significant variables actually affect the response. Calculate the ideal settings for each significant element by quantifying its effect size. 

To ensure a thorough grasp of how various variables affect the result, evaluate the interactions between components and ascertain their impact on the response.

Implement Solutions with Data-Driven Confidence

Start by creating workable solutions based on the findings of your study in order to execute solutions with confidence that is informed by evidence. These fixes could include updating designs, introducing new tactics, altering formulas, and adjusting process settings. 

To make sure the solutions are effective, validate them with more trials or pilot studies. After the solutions are put into place, keep an eye on them and evaluate their effects over time. Use the information gathered to make any necessary additional improvements or modifications.

DoE in Testing

The field of testing has seen a revolution in the evaluation and optimization of products and processes thanks to the Design of Experiments (DoE) approach. It offers a methodical and effective way to look into the various ways that variable inputs affect a system's quality, dependability, and performance across a broad spectrum of circumstances.

Why DoE is Essential for Testing

Traditional testing methods often involve changing one factor at a time, which can be time-consuming and may miss critical interactions between factors. DoE, on the other hand, allows testers to simultaneously manipulate multiple factors according to a carefully designed plan. 

This enables them to:

Identify Optimal Settings

DoE helps determine the combination of factor settings that yield the best possible results, whether it's maximizing a desired output (e.g., yield, efficiency) or minimizing an undesirable one (e.g., defects, variability).

Reduce Variability

DoE can assist in identifying methods to lessen or regulate system performance variability by understanding the various elements that contribute to this variability and how to achieve more consistent and predictable results.

Enhance Robustness

DoE can identify solutions that are robust to variations in factors, ensuring that the product or process performs well even under different operating conditions or with varying inputs.

Accelerate Testing

DoE can save time and money by strategically choosing experimental runs and evaluating the collected data, which can lower the number of experiments needed to produce trustworthy results.

Gain Deeper Insights

DoE provides a deeper knowledge of the behavior of the system by revealing intricate interconnections between components, going beyond just identifying key ones.

Examples of DoE in Testing

Here are a few examples of DoE in testing that you might find useful:

Software Testing

DoE is used to optimize software performance , identify bugs and vulnerabilities, and ensure compatibility across different platforms and configurations. For example, a software company might use DoE to test the impact of different hardware configurations, network conditions, and user behaviors on the performance of their application.

Product Testing

DoE is employed to evaluate the performance and reliability of products under various conditions, such as temperature, humidity, vibration, and stress. This helps manufacturers identify design weaknesses, improve product robustness, and ensure compliance with quality standards. For instance, an electronics company might use DoE to test the durability of their smartphones under extreme temperatures and humidity levels.

Process Testing

DoE is applied to optimize manufacturing processes, improve yield, reduce defects, and enhance overall efficiency. For example, a chemical company might use DoE to optimize the reaction conditions for a chemical synthesis process, such as temperature, pressure, and reactant concentrations.

Medical Device Testing

DoE is used to assess the effectiveness and safety of medical devices across a variety of patient groups, usage scenarios, and environmental settings. This ensures that medical gadgets function consistently well in real-world circumstances and satisfy regulatory standards.

A flexible approach, Design of Experiments enables organizations to solve complicated challenges, obtain deeper insights, and make data-driven decisions. You can reach a new level of productivity and creativity in your industry by adopting DoE and making use of the appropriate software solutions.

In search of DoE Courses? From introductory to advanced courses in Design of Experiments , SkillTrans has a lot to offer. Look through our collection to select the ideal training to advance your knowledge!

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• Science Snippets Blog

What is DOE? Design of Experiments Basics for Beginners

[This blog was a favorite last year, so we thought you'd like to see it again. Send us your comments!]. Whether you work in engineering, R&D, or a science lab, understanding the basics of experimental design can help you achieve more statistically optimal results from your experiments or improve your output quality.

This article is posted on our Science Snippets Blog .

Using  Design of Experiments (DOE)  techniques, you can determine the individual and interactive effects of various factors that can influence the output results of your measurements. You can also use DOE to gain knowledge and estimate the best operating conditions of a system, process or product.

DOE applies to many different investigation objectives, but can be especially important early on in a screening investigation to help you determine what the most important factors are. Then, it may help you optimize and better understand how the most important factors that you can regulate influence the responses or critical quality attributes.

Another important application area for DOE is in making production more effective by identifying factors that can reduce material and energy consumption or minimize costs and waiting time. It is also valuable for robustness testing to ensure quality before releasing a product or system to the market.

What’s the Alternative?

In order to understand why Design of Experiments is so valuable, it may be helpful to take a look at what DOE helps you achieve. A good way to illustrate this is by looking at an alternative approach, one that we call the  “COST”  approach. The COST ( C hange  O ne  S eparate factor at a  T ime) approach might be considered an intuitive or even logical way to approach your experimentation options (until, that is, you have been exposed to the ideas and thinking of DOE).

Let’s consider the example of a small chemical reaction where the goal is to find optimal conditions for yield. In this example, we can vary only two elements, or factors:

• the volume of the reaction container (between 500 and 700 ml), and
• the pH of the solution (between 2.5 and 5).

We change the experimental factors and measure the response outcome, which in this case, is the yield of the desired product. Using the COST approach, we can vary just one of the factors at time to see what affect it has on the yield.

So, for example, first we might fix the pH at 3, and change the volume of the reaction container from a low setting of 500ml to a high of 700ml. From that we can measure the yield.

Below is an example of a table that shows the yield that was obtained when changing the volume from 500 to 700 ml. In the scatterplot on the right, we have plotted the measured yield against the change in reaction volume, and it doesn’t take long to see that the best volume is located at 550 ml.

Next, we evaluate what will happen when we fix the volume at 550 ml (the optimal level) and start to change the second factor. In this second experimental series, the pH is changed from 2.5 to 5.0 and you can see the measured yields. These are listed in the table and plotted below. From this we can see that the optimal pH is around 4.5.

The optimal combination for the best yield would be a volume of 550 ml and pH 4.5. Sounds good right? But, let’s consider this a bit more.

Gaining a Better Perspective With DOE

What happens when we take more of a bird’s eye perspective, and look at the overall experimental map by number and order of experiments?

For example, in the first experimental series (indicated on the horizontal axis below), we moved the experimental settings from left to right, and we found out that 550 was the optimal volume.

Then in the second experimental series, we moved from bottom to top (as shown in the scatterplot below) and after a while we found out that the best yield was at experiment number 10 (4.5 pH).

The problem here is that we are not really certain whether the experimental point number 10 is truly the best one. The risk is that we have perceived that as being the optimum without it really being the case. Another thing we may question is the number of experiments we used. Have we used the optimal number of runs for experiments?

Zooming out and picturing what we have done on a map, we can see that we have only been exploiting a very small part of the entire experimental space. The true relationship between pH and volume is represented by the Contour Plot pictured below. We can see that the optimal value would be somewhere at the top in the larger red area.

So the problem with the COST approach is that we can get very different implications if we choose other starting points. We perceive that the optimum was found, but the other— and perhaps more problematic thing—is that we didn’t realize that continuing to do additional experiments would produce even higher yields.

How to Design Better Experiments

Instead, using the DOE approach, we can build a map in a much better way. First, consider the use of just two factors, which would mean that we have a limited range of experiments.  As the contour plot below shows, we would have at least four experiments (defining the corners of a rectangle.)

These four points can be optimally supplemented by a couple of points representing the variation in the interior part of the experimental design.

The important thing here is that when we start to evaluate the result, we will obtain very valuable information about the direction in which to move for improving the result. We will understand that we should reposition the experimental plan according to the dashed arrow.

However, DOE is NOT limited to looking at just two factors. It can be applied to three, four or many more factors.

If we take the approach of using three factors, the experimental protocol will start to define a cube rather than a rectangle. So the factorial points will be the corners of the cube.

In this way, DOE allows you to construct a carefully prepared set of representative experiments, in which all relevant factors are varied simultaneously.

DOE is about creating an entity of experiments that work together to map an interesting experimental region. So with DOE we can prepare a set of experiments that are optimally placed to bring back as much information as possible about how the factors are influencing the responses.

Plus, we will we have support for different types of regression models. For example, we can estimate what we call a linear model, or an interaction model, or a quadratic model. So the selected experimental plan will support a specific type of model.

Why Is DOE a Better Approach?

We can see three main reasons that DOE Is a better approach to experiment design than the COST approach.

DOE suggests the correct number of runs needed (often fewer than used by the COST approach)

DOE provides a model for the direction to follow

Many factors can be used (not just two)

In summary, the benefits of DOE are:

• An organized approach that connects experiments in a rational manner
• The influence of and interactions between all factors can be estimated
• More precise information is acquired in fewer experiments
• Results are evaluated in the light of variability
• Support for decision-marketing: map of the system (response contour plot)

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What is Design of Experiments (DOE)?

• Design of Experiments is a framework that allows us to investigate the impact of multiple different factors on an experimental process
• It identifies and explores the interactions between factors and allows researchers to optimize the performance and robustness of processes or assays
• The old conventional approach to scientific experimentation (one-factor-at-a-time, or “OFAT”) are limited in both the number of variables which you can investigate and, critically, preclude investigating how variables interact
• This blog introduces the principles of Design of Experiments, beginning with its origins
• If you’d like to keep learning about DOE after you're done with this article, make sure to  check out our other DOE blogs , download our  DOE for biologists ebook , or watch our  DOE Masterclass webinar series .

DOE Masterclass (Part 1)

What doe is and how it transforms your biological research.

A richer understanding of biological complexity .

What makes a good cup of tea?

A discussion about whether adding milk before or after the tea influences the taste may seem a long way from ensuring that Escherichia coli  expresses a particular plasmid, optimizing vaccine formulation and delivery, 1,2 or dissecting the intricacies of metabolomics. 3  

But it's closer than you think.

After all, scientific revolutions can arise from everyday observations: a falling apple inspired Isaac Newton to formulate gravitational theory.

Of all the places for a revolution to start, a tea party in 1920s Cambridge laid the foundations of a statistical technique called Design of Experiments (DOE), which allows researchers to investigate the impact of simultaneously changing multiple factors.

Design of Experiments (DOE): a surprising origin story .

One afternoon some dons, their wives, and guests were having afternoon tea. One lady said she could taste whether tea or milk was poured into the cup first. (Some people believe that hot tea scorches milk, for example.)

The statistician Ronald Fisher, who attended the tea party, devised an experiment to test her claim. The lady was randomly given four cups in which tea was poured before the milk and four where the milk was poured first.

To analyze the interactions between the factors (milk and tea), Ronald devised Fisher’s Exact Test. This determines if any association between the two categorical variables is statistically significant. 4  

As Figure 1 shows, even four cups of tea can give rise to numerous possible permutations. But this only scratches the surface of tea–making’s complexity.

A perfect cup of tea depends on multiple other factors, such as the blend, brewing time, and the addition of sugar. In other words, making a perfect cup of tea is complex and multidimensional. DOE allows researchers to investigate the effect of changing multiple factors simultaneously.

0= Incorrect; X=correct

Figure 1: Distribution factors assuming that the lady could not distinguish that milk was added before tea (null hypothesis)

In a series of blogs, we’re going to explore the basis of DOE, who should consider DOE, and some ways in which this methodology helps experimental biologists deal with life’s inherent complexity. We’ll begin, however, by going back to school.

School's out... and so is OFAT (one-factor-at-a-time) experimentation .

Our school teachers advocated a one-factor-at-a-time (OFAT) approach to scientific experimentation. So, pick a variable (factor) and vary the value (levels), while keeping everything else constant. 

That may be fine in the school lab. Unfortunately, biology doesn’t work that way .

Biological variation, for example, can mean results vary randomly around a set point even in a constant environment. Sample collection, transport, preservation, and measurement systems can introduce further sources of variation. 5  

DOE helps us understand emergent phenomena .

Biological phenomena, even life itself, are typically emergent . In other words, new patterns and structures appear through the interactions between autonomous elements. 6

Every living thing consists of numerous autonomous parts that interact dynamically and unpredictably as part of one or more systems. This means, for example, that you can’t predict cellular diversity by examining nucleotides’ chemical and physical properties.

You also can’t predict the products of cognition by analyzing neuroarchitecture. Emergence is one reason biologists often lack well-developed, robust theoretical frameworks to guide their experiments.

DOE is better for exploring biological complexity .

Most biological processes are complicated, complex, and multidimensional. 7 So, changing one factor probably changes something else .

For example, it isn't possible to fully understand the functional consequences of changing a protein's structure without understanding all the contexts in which it appears. Its interactions within biological networks are what really define its function, so even minor changes can produce a plethora of unpredictable down- and upstream effects.

DOE allows the explorations of complex, multidimensional experimental design spaces despite such methodological, biological, or chemical variations. 7  

OFAT ignores biology’s inherent complexity . It is limited in both the number of variables that you can investigate and, critically, it precludes any investigation of how variables interact.

It’s a bit like trying to analyze the perfect cup of tea by ignoring the temperature of the water, brew time, and blend, and instead just focusing on whether you add the milk first or second. 

Figure 2: OFAT may convince you you’ve found an optimum… but it may not be the real one.

Unsurprisingly, OFAT can often identify the wrong system state as the optimum .

Moreover, the lack of well-developed, robust theoretical frameworks can result in unconscious cognitive bias: it’s all too easy to develop OFAT experiments that confirm, rather than test, hypotheses. 7

DOE helps avoid unconscious cognitive bias and allows researchers to look behind the curtain of biological complexity to see what’s really going on.

What is Design of Experiments (DOE) ?

Design of Experiments is a framework that allows us to investigate the impact of multiple different factors—changed simultaneously—on an experimental process .

DOE also identifies and explores the interactions between those factors. This allows us to optimize the performance and robustness of our processes or assays.

Let’s apply DOE to another simple example: the strawberries you may have with the tea you’ve just added your milk to... 

DOE looks at different ranges within factors .

Numerous quantitative factors (e.g. hours of sunlight, grams of plant food, and liters of water) or qualitative factors (e.g. the cultivar) can influence the strawberry crop ( Figure 2 ).

You need to begin by setting a realistic range for each factor. So, testing 1kg of plant food could prove toxic and expensive. Strawberries also need plenty of water to ensure juiciness; applying 1ml of water would be difficult to accurately achieve and, possibly, trigger drought stress responses.

Figure 3: Design of Experiments (DOE) through the example of strawberries. How different factors and levels may impact the yield, weight, and taste of a crop of strawberries

DOE tests many factors at the same time .

The responses we are looking for in this experiment are the yield, the weight, and the taste of the strawberries. You may decide you want a high yield of the tastiest strawberries. 

Design of experiments allows you to test numerous factors to determine which make the largest contributions to yield and taste.

Based on this, you can fine-tune the experiment and use DOE to determine which combination of factors at specific levels gives the optimal balance of yield and taste.

You can also compare different levels for given factors, such as whether a cultivar from nursery A produces a higher yield, better taste, or both than a plant from nursery B.

DOE lets you investigate specific outcomes .

Design of Experiments also allows you to investigate specific outcomes (what combinations produce the best balance of yield and taste in a robust way) and reduce variability (define new conditions so the strawberry yield remains the same).

Cost may be another consideration. DOE lets you balance trade-offs , such as what conditions produce the most cost-effective way to achieve the highest yield of strawberries.

DOE Masterclass: Design of Experiments 101 for biologists .

DOE helps reduce the time, materials, and experiments needed to yield a given amount of information compared with OFAT.

As well as these savings, DOE achieves higher precision and reduced variability when estimating the effects of each factor or interaction than using OFAT. It also systematically estimates the interaction between factors, which is not possible with OFAT experiments.

This article offers only a very brief introduction to DOE.

Dive deeper into Design of Experiments:

• Why should I use Design of Experiments in Life Sciences

When and how to use Design of Experiments (DOE)

• DOE in the real world: when and how to use Design of Experiments
• Types of DOE design: a users' guide
• The DOE process: an overview
• Overcoming barriers to Design of Experiments (DOE)
• 3 reasons why DOE rollouts fail and what to do about it
• Four ways to cut R&D costs with DOE

Well, I’m off for a cup of tea.

Interested in learning more about DOE? Download our  DOE for biologists ebook , or watch our  DOE Masterclass webinar series . Catch the full series of recordings on our YouTube page .

• Ahl PL, Mensch C, Hu B et al. Accelerating vaccine formulation development using design of experiment stability studies. Journal of Pharmaceutical Sciences 2016;105:3046-3056
• Hashiba A, Toyooka M, Sato Y et al. The use of design of experiments with multiple responses to determine optimal formulations for in vivo hepatic mRNA delivery. Journal of Controlled Release 2020;327:467-476
• Surowiec I, Johansson E, Torell F et al. Multivariate strategy for the sample selection and integration of multi-batch data in metabolomics. Metabolomics 2017;13:114
• Bi J and Kuesten C. Revisiting Fisher’s ‘Lady Tasting Tea’ from a perspective of sensory discrimination testing. Food Quality and Preference 2015;43:47-52
• Badrick T. Biological variation: Understanding why it is so important? Practical Laboratory Medicine 2021;23:e00199
• Ikegami T, Mototake Y-i, Kobori S et al. Life as an emergent phenomenon: studies from a large-scale boid simulation and web data. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 2017;375:20160351
• Lendrem DW, Lendrem BC, Woods D et al. Lost in space: design of experiments and scientific exploration in a Hogarth Universe. Drug Discovery Today 2015;20:1365-1371

Michael "Sid" Sadowski, PhD

Michael Sadowski, aka Sid, is the Director of Scientific Software at Synthace, where he leads the company’s DOE product development. In his 10 years at the company he has consulted on dozens of DOE campaigns, many of which included aspects of QbD.

Other posts you might be interested in

Why Design of Experiments (DOE) is important for biologists

Why quality by design (qbd) is vital for pharmaceutical r&d.

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What is Design of Experiments (DOE)? Your Method to Optimize Results

Learn about Design of Experiments and how it can help you achieve optimal results from your experiments

What is Design of Experiments (DOE)?

Design of Experiments (DOE) is a systematic method used in applied statistics to evaluate the many possible alternatives in one or more design variables. It allows the manipulation of various input variables (factors) to determine what effect they could have in order to get the desired output (responses) or improve on the result.

In DoE, experiments are being used to find an unknown outcome or effect, to test a theory, or to demonstrate an already known effect. T hey are done by scientists and engineers, among others, in order to understand which inputs have a major impact on output and what input levels should be targeted to reach a desired outcome (output). Simply put, DoE is a way to collect information during the experiment and then determine what factors or which processes could lead to the desired result.

History of Design of Experiments

The term “Design of Experiments,” also known as experimental design, was coined by Ronald Fisher in the 1920s. He used it to describe a method of planning experiments to find the best combination of factors that affect the response or output. It is used to reduce design expenses because analysis of input parameters or factors gives way in identifying waste and which processes can be eliminated. It also helps remove complexities and streamlining the design process for cost management in the manufacturing process.

The key concept behind this methodology is that there is a relationship between the factors affecting the response. ISixSigma defined it as determining the “cause and effect relationships” of factors. Therefore, a complete experimental plan consists of the combination of factors used to evaluate their effects on the response.

Components of Experimental Design

MoreSteam gave a simple illustration to explain the components of the experiment—the three aspects that need to be analyzed in the design experiments—and understanding the meaning of each is crucial in defining DoE.

Cake-baking Process showing the Components of Experimental Design source: MoreSteam

• Controllable variables – pertains to factors that can be modified or changed in an experiment or a process. For example, in the cake-baking process, these factors may include what will be used in baking such as the oven, sugar, flour, and eggs.
• Uncontrollable variables – pertains to factors that cannot be changed. For example, in the cake baking process, this may be the room temperature in the kitchen. They must be recognized to understand how they may affect the response.
• Levels or settings of each factor – they pertain to the quantity or quality that will be used in the experiment. In the cake-baking process example, this includes the oven temperature setting and the quantity of sugar, flour, and eggs.
• Responses – pertains to the outcome of the process that gages the desired effect. In the cake-baking example, the taste, appearance, and consistency of the cake are the responses. They are influenced by the factors and their levels. This is the purpose of experimentation—analyzing each factor to determine which of them provides the best overall outcome or the same quality.

Purpose of Design of Experiments

Experimental design is not only conducted by scientists or engineers. It can be used by different industries who want to maximize the results they’re getting. DoE is conducted to:

Compare alternatives

Conducting experimental design allows you to look at different alternatives. It helps in making an informed decision on what to use or what to change. This methodology can also be used to discover the best combination of alternatives in the experiment.

Maximize process response

With DoE, the factors and their levels are checked and see which of them when used are giving the exact quality in the response.

Reduce variations

Excess variations in the process are the cause of added expense. It affects the cycle time that causes quality differences. With DoE, factors are identified, responses are interpreted, and waste is eliminated or changed.

Process Improvement

Performing a DOE can uncover significant issues that are typically missed when conducting an experiment. These areas will be corrected thus improving the process.

Evaluate the effect of change/s

With DoE, you can determine the effects of changes made with the factors and their levels that influences the response.

Quality Control

DOE can also help improve manufacturing efficiency by identifying factors that reduce material and energy use, costs, and waiting time. It is also used to test a product or system before releasing it to market.

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Examples and Applications of Experimental Design

Below are some practical applications or examples on where DoE is applied:

Pharmaceutical Industry

In the pharmaceutical industry, DOE is most typically used throughout the drug formulation and manufacturing phases. Qualitty is critical for drug products because health and safety of consumers are at risk when a product doesn’t meet the standards. DoE is used in drug testing, reducing impurities in the process of making drugs, before releasing it for consumer use.

DoE is used especially in drugs that are best delivered via a time-release schedule,. It means that it takes time to dissolve slowly in the body. Because one component of DoE is the settings of factors, performing an experimental runs are applicable here.

Fast-Moving Consumer Goods (FMCG) industry

FMCG industry is a part of consumer goods industry that includes all the products which are sold to the general public by any means such as retail stores, internet or by phone. These are mostly used by the consumers in their daily life and may include food, drinks, health and hygiene, cosmetics, household appliances, among others. DoE helps in comparing alternatives or options to get the response where price will be cheaper but does not compromise on quality.

Product Design

DoE is a useful tool for determining specific factors affecting defect levels in a product, which may be used to improve the design of the product.

6 Steps Design of Experiments

Standard DoE processes are often structured around seven or fewer steps. The steps in experimental design will take you through the process of determining what is the best response that you could use in your study, workplace, or procedures.

Steps of Design of Experiments (DOE). Source: JMP

• Describe – this is a critical part wherein you determine what is your goal or what do you want to achieve, which is followed by determining what is your desired response. The first step includes determining your goal, your desired response, and factors.
• Specify – this is the part where you need to specify what variables describe the physical situation, or the factors.
• Design – this is the part where you generate an experimental design model from which you will draw evaluations after run/s or trial/s.
• Collect– this is the part where you execute the design, collect information from the run/s and record the responses that you get.
• Fit – this is the part where you review the responses if it does fit in the generated experimental design model. In some cases, runs should be repeated in order to correct model ambiguity.
• Predict – the last step wherein you predict the results and determine which factor best optimizes the response.

SafetyCulture (formerly iAuditor) for Experimental Design

Why safetyculture.

Perform a DoE to optimize any procedure in your workplace and integrate your experimentation with SafetyCulture . A powerful tool used by multiple industries in performing a more convenient and efficient way to monitor, collect, record, inspect, and audit data.

With the support of SafetyCulture as a Design of Experiments software , engineers, scientists, manufacturers, and researchers, among others, can do the following during the experimental design:

• Monitor and identify if there are process drifts and changes in variables during the run with sensors and the monitoring feature.
• Record the responses that you generate through your experimental runs in a secured cloud and easily access it anywhere when needed through the app.
• Specify which factors have defects using Quality Control Check Sheet.
• Modify quality inspections templates tailored to your specifications to support your experimentation.
• Notify or alert your team about modifications on data collected real-time.

Browse checklists helpful to experimental design:

• DMAIC Template Checklist
• Manufacturing Quality Control Checklist
• Product Evaluation Template Checklist
• DMADV Template Checklist

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Maximizing Efficiency and Accuracy with Design of Experiments

Updated: April 21, 2024 by Ken Feldman

Design of experiments (DOE) can be defined as a set of statistical tools that deal with the planning, executing, analyzing, and interpretation of controlled tests to determine which factors will impact and drive the outcomes of your process. 

This article will explore two of the common approaches to DOE as well as the benefits of using DOE and offer some best practices for a successful experiment. 

Overview: What is DOE? 

Two of the most common approaches to DOE are a full factorial DOE and a fractional factorial DOE . Let’s start with a discussion of what a full factorial DOE is all about.

The purpose of the full factorial DOE is to determine at what settings of your process inputs will you optimize the values of your process outcomes. As an example, if your output is the fill level of a bottle of carbonated drink, and your primary process variables are machine speed, fill speed, and carbonation level, then what combination of those factors will give you the desired consistent fill level of the bottle?

With three variables, machine speed, fill speed, and carbonation level, how many different unique combinations would you have to test to explore all the possibilities? Which combination of machine speed, fill speed, and carbonation level will give you the most consistent fill? The experimentation using all possible factor combinations is called a full factorial design. These combinations are called Runs .  

We can calculate the total number of runs using the formula # Runs=2^k, where k is the number of variables and 2 is the number of levels, such as (High/Low) or (100 ml per minute/200 ml per minute). 

But, what if you aren’t able to run the entire set of combinations of a full factorial? What if you have monetary or time constraints, or too many variables? This is when you might choose to run a fractional factorial , also referred to as a screening DOE , which uses only a fraction of the total runs. That fraction can be one-half, one-quarter, one-eighth, and so forth depending on the number of factors or variables. 

While there is a formula to calculate the number of runs, suffice it to say you can just calculate your full factorial runs and divide by the fraction that you and your Black Belt or Master Black Belt determine is best for your experiment.

3 benefits of DOE 

Doing a designed experiment as opposed to using a trial-and-error approach has a number of benefits.  

1. Identify the main effects of your factors

A main effect is the impact of a specific variable on your output. In other words, how much does machine speed alone impact your output? Or fill speed?

2. Identifying interactions

Interactions occur if the impact of one factor on your response is dependent upon the setting of another factor. For example if you ran at a fill speed of 100 ml per minute, what machine speed should you run at to optimize your fill level? Likewise, what machine speed should you run at if your fill speed was 200 ml per minute? 

A full factorial design provides information about all the possible interactions. Fractional factorial designs will provide limited interaction information because you did not test all the possible combinations. 

3. You can determine optimal settings for your variables 

After analyzing all of your main effects and interactions, you will be able to determine what your settings should be for your factors or variables. 

Why is DOE important to understand? 

When discussing the proper settings for your process variables, people often rely on what they have always done, on what Old Joe taught them years ago, or even where they feel the best setting should be. DOE provides a more scientific approach. 

Distinguish between significant and insignificant factors

Your process variables have different impacts on your output. Some are statistically important, and some are just noise. You need to understand which is which.

The existence of interactions

Unfortunately, most process outcomes are a function of interactions rather than pure main effects. You will need to understand the implications of that when operating your processes. 

Statistical significance 

DOE statistical outputs will indicate whether your main effects and interactions are statistically significant or not. You will need to understand that so you focus on those variables that have real impact on your process.

An industry example of DOE 

A unique application of DOE in marketing is called conjoint analysis. A web-based company wanted to design its website to increase traffic and online sales. Doing a traditional DOE was not practical, so leadership decided to use conjoint analysis to help them design the optimal web page.

The marketing and IT team members identified the following variables that seemed to impact their users’ online experience: 

• loading speed of the site
• font of the text
• color scheme
• primary graphic motion
• primary graphic size 
• menu orientation

They enlisted the company’s Master Black Belt to help them do the experiment using a two-level approach.

In a conjoint analysis DOE, you would create mockups of the various combinations of variables. A sample of customers were selected and shown the different mockups. After viewing them, the customer then ranked the different mockups from most preferred to least preferred. The ranking provided the numerical value of that combination. To keep matters simple, they went with a quarter fraction design, or 16 different mockups. Otherwise, you’re asking customers to try and differentiate their preference and rank way too many options.

Once they gathered all the data and analyzed it, they concluded that menu orientation and loading speed were the most significant factors. This allowed them to do what they wanted with font, primary graphic, and color scheme since they were not significant.

3 best practices when thinking about DOE 

Experiments take planning and proper execution, otherwise the results may be meaningless. Here are a few hints for making sure you properly run your DOE. 

1. Carefully identify your variables

Use existing data and data analysis to try and identify the most logical factors for your experiment. Regression analysis is often a good source of selecting potentially significant factors. 

2. Prevent contamination of your experiment

During your experiment, you will have your experimental factors as well as other environmental factors around you that you aren’t interested in testing. You will need to control those to reduce the noise and contamination that might occur (which would reduce the value of your DOE).

3. Use screening experiments to reduce cost and time

Unless you’ve done some prior screening of your potential factors, you might want to start your DOE with a screening or fractional factorial design. This will provide information as to potentially significant factors without consuming your whole budget. Once you’ve identified the best potential factors, you can do a full factorial with the reduced number of factors.

Frequently Asked Questions (FAQ) about DOE

What does “main effects” refer to.

The main effects of a DOE are the individual factors that have a statistically significant effect on your output. In the common two-level DOE, an effect is measured by subtracting the response value for running at the high level from the response value for running at the low level. The difference is the effect of that factor.

How many runs do I need for a full factorial DOE?

The formula for calculating the number of runs of a full factorial DOE is # Runs=X^K where X is the number of levels or settings, and K is the number of variables for factors.

Are interactions in DOE important? 

Yes. Sometimes your DOE factors do not behave the same way when you look at them together as opposed to looking at the factor impact individually. In the world of pharmaceuticals, you hear a lot about drug interactions. You can safely take an antihistamine for your allergies. You can also safely take an antibiotic for your infection. But taking them both at the same time can cause an interaction effect that can be deadly.

In summary, DOE is the way to go

A design of experiments (DOE) is a set of statistical tools for planning, executing, analyzing, and interpreting experimental tests to determine the impact of your process factors on the outcomes of your process. 

The technique allows you to simultaneously control and manipulate multiple input factors to determine their effect on a desired output or response. By simultaneously testing multiple inputs, your DOE can identify significant interactions you might miss if you were only testing one factor at a time. 

You can either use full factorial designs with all possible factor combinations, or fractional factorial designs using smaller subsets of the combinations.

About the Author

Ken Feldman

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• A Quick Guide to Experimental Design | 5 Steps & Examples

A Quick Guide to Experimental Design | 5 Steps & Examples

Published on 11 April 2022 by Rebecca Bevans . Revised on 5 December 2022.

Experiments are used to study causal relationships . You manipulate one or more independent variables and measure their effect on one or more dependent variables.

Experimental design means creating a set of procedures to systematically test a hypothesis . A good experimental design requires a strong understanding of the system you are studying. 

There are five key steps in designing an experiment:

• Consider your variables and how they are related
• Write a specific, testable hypothesis
• Design experimental treatments to manipulate your independent variable
• Assign subjects to groups, either between-subjects or within-subjects
• Plan how you will measure your dependent variable

For valid conclusions, you also need to select a representative sample and control any  extraneous variables that might influence your results. If if random assignment of participants to control and treatment groups is impossible, unethical, or highly difficult, consider an observational study instead.

Table of contents

Step 1: define your variables, step 2: write your hypothesis, step 3: design your experimental treatments, step 4: assign your subjects to treatment groups, step 5: measure your dependent variable, frequently asked questions about experimental design.

You should begin with a specific research question . We will work with two research question examples, one from health sciences and one from ecology:

To translate your research question into an experimental hypothesis, you need to define the main variables and make predictions about how they are related.

Start by simply listing the independent and dependent variables .

Then you need to think about possible extraneous and confounding variables and consider how you might control  them in your experiment.

Finally, you can put these variables together into a diagram. Use arrows to show the possible relationships between variables and include signs to show the expected direction of the relationships.

Here we predict that increasing temperature will increase soil respiration and decrease soil moisture, while decreasing soil moisture will lead to decreased soil respiration.

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Now that you have a strong conceptual understanding of the system you are studying, you should be able to write a specific, testable hypothesis that addresses your research question.

The next steps will describe how to design a controlled experiment . In a controlled experiment, you must be able to:

• Systematically and precisely manipulate the independent variable(s).
• Precisely measure the dependent variable(s).
• Control any potential confounding variables.

If your study system doesn’t match these criteria, there are other types of research you can use to answer your research question.

How you manipulate the independent variable can affect the experiment’s external validity – that is, the extent to which the results can be generalised and applied to the broader world.

First, you may need to decide how widely to vary your independent variable.

• just slightly above the natural range for your study region.
• over a wider range of temperatures to mimic future warming.
• over an extreme range that is beyond any possible natural variation.

Second, you may need to choose how finely to vary your independent variable. Sometimes this choice is made for you by your experimental system, but often you will need to decide, and this will affect how much you can infer from your results.

• a categorical variable : either as binary (yes/no) or as levels of a factor (no phone use, low phone use, high phone use).
• a continuous variable (minutes of phone use measured every night).

How you apply your experimental treatments to your test subjects is crucial for obtaining valid and reliable results.

First, you need to consider the study size : how many individuals will be included in the experiment? In general, the more subjects you include, the greater your experiment’s statistical power , which determines how much confidence you can have in your results.

Then you need to randomly assign your subjects to treatment groups . Each group receives a different level of the treatment (e.g. no phone use, low phone use, high phone use).

You should also include a control group , which receives no treatment. The control group tells us what would have happened to your test subjects without any experimental intervention.

When assigning your subjects to groups, there are two main choices you need to make:

• A completely randomised design vs a randomised block design .
• A between-subjects design vs a within-subjects design .

Randomisation

An experiment can be completely randomised or randomised within blocks (aka strata):

• In a completely randomised design , every subject is assigned to a treatment group at random.
• In a randomised block design (aka stratified random design), subjects are first grouped according to a characteristic they share, and then randomly assigned to treatments within those groups.

Sometimes randomisation isn’t practical or ethical , so researchers create partially-random or even non-random designs. An experimental design where treatments aren’t randomly assigned is called a quasi-experimental design .

Between-subjects vs within-subjects

In a between-subjects design (also known as an independent measures design or classic ANOVA design), individuals receive only one of the possible levels of an experimental treatment.

In medical or social research, you might also use matched pairs within your between-subjects design to make sure that each treatment group contains the same variety of test subjects in the same proportions.

In a within-subjects design (also known as a repeated measures design), every individual receives each of the experimental treatments consecutively, and their responses to each treatment are measured.

Within-subjects or repeated measures can also refer to an experimental design where an effect emerges over time, and individual responses are measured over time in order to measure this effect as it emerges.

Counterbalancing (randomising or reversing the order of treatments among subjects) is often used in within-subjects designs to ensure that the order of treatment application doesn’t influence the results of the experiment.

Finally, you need to decide how you’ll collect data on your dependent variable outcomes. You should aim for reliable and valid measurements that minimise bias or error.

Some variables, like temperature, can be objectively measured with scientific instruments. Others may need to be operationalised to turn them into measurable observations.

• Ask participants to record what time they go to sleep and get up each day.
• Ask participants to wear a sleep tracker.

How precisely you measure your dependent variable also affects the kinds of statistical analysis you can use on your data.

Experiments are always context-dependent, and a good experimental design will take into account all of the unique considerations of your study system to produce information that is both valid and relevant to your research question.

Experimental designs are a set of procedures that you plan in order to examine the relationship between variables that interest you.

To design a successful experiment, first identify:

• A testable hypothesis
• One or more independent variables that you will manipulate
• One or more dependent variables that you will measure

When designing the experiment, first decide:

• How your variable(s) will be manipulated
• How you will control for any potential confounding or lurking variables
• How many subjects you will include
• How you will assign treatments to your subjects

The key difference between observational studies and experiments is that, done correctly, an observational study will never influence the responses or behaviours of participants. Experimental designs will have a treatment condition applied to at least a portion of participants.

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

In a between-subjects design , every participant experiences only one condition, and researchers assess group differences between participants in various conditions.

In a within-subjects design , each participant experiences all conditions, and researchers test the same participants repeatedly for differences between conditions.

The word ‘between’ means that you’re comparing different conditions between groups, while the word ‘within’ means you’re comparing different conditions within the same group.

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Experimental Design: Types, Examples & Methods

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

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Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

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Experimental design refers to how participants are allocated to different groups in an experiment. Types of design include repeated measures, independent groups, and matched pairs designs.

Probably the most common way to design an experiment in psychology is to divide the participants into two groups, the experimental group and the control group, and then introduce a change to the experimental group, not the control group.

The researcher must decide how he/she will allocate their sample to the different experimental groups.  For example, if there are 10 participants, will all 10 participants participate in both groups (e.g., repeated measures), or will the participants be split in half and take part in only one group each?

Three types of experimental designs are commonly used:

1. Independent Measures

Independent measures design, also known as between-groups , is an experimental design where different participants are used in each condition of the independent variable.  This means that each condition of the experiment includes a different group of participants.

This should be done by random allocation, ensuring that each participant has an equal chance of being assigned to one group.

Independent measures involve using two separate groups of participants, one in each condition. For example:

• Con : More people are needed than with the repeated measures design (i.e., more time-consuming).
• Pro : Avoids order effects (such as practice or fatigue) as people participate in one condition only.  If a person is involved in several conditions, they may become bored, tired, and fed up by the time they come to the second condition or become wise to the requirements of the experiment!
• Con : Differences between participants in the groups may affect results, for example, variations in age, gender, or social background.  These differences are known as participant variables (i.e., a type of extraneous variable ).
• Control : After the participants have been recruited, they should be randomly assigned to their groups. This should ensure the groups are similar, on average (reducing participant variables).

2. Repeated Measures Design

Repeated Measures design is an experimental design where the same participants participate in each independent variable condition.  This means that each experiment condition includes the same group of participants.

Repeated Measures design is also known as within-groups or within-subjects design .

• Pro : As the same participants are used in each condition, participant variables (i.e., individual differences) are reduced.
• Con : There may be order effects. Order effects refer to the order of the conditions affecting the participants’ behavior.  Performance in the second condition may be better because the participants know what to do (i.e., practice effect).  Or their performance might be worse in the second condition because they are tired (i.e., fatigue effect). This limitation can be controlled using counterbalancing.
• Pro : Fewer people are needed as they participate in all conditions (i.e., saves time).
• Control : To combat order effects, the researcher counter-balances the order of the conditions for the participants.  Alternating the order in which participants perform in different conditions of an experiment.

Counterbalancing

Suppose we used a repeated measures design in which all of the participants first learned words in “loud noise” and then learned them in “no noise.”

We expect the participants to learn better in “no noise” because of order effects, such as practice. However, a researcher can control for order effects using counterbalancing.

The sample would be split into two groups: experimental (A) and control (B).  For example, group 1 does ‘A’ then ‘B,’ and group 2 does ‘B’ then ‘A.’ This is to eliminate order effects.

Although order effects occur for each participant, they balance each other out in the results because they occur equally in both groups.

3. Matched Pairs Design

A matched pairs design is an experimental design where pairs of participants are matched in terms of key variables, such as age or socioeconomic status. One member of each pair is then placed into the experimental group and the other member into the control group .

One member of each matched pair must be randomly assigned to the experimental group and the other to the control group.

• Con : If one participant drops out, you lose 2 PPs’ data.
• Pro : Reduces participant variables because the researcher has tried to pair up the participants so that each condition has people with similar abilities and characteristics.
• Con : Very time-consuming trying to find closely matched pairs.
• Pro : It avoids order effects, so counterbalancing is not necessary.
• Con : Impossible to match people exactly unless they are identical twins!
• Control : Members of each pair should be randomly assigned to conditions. However, this does not solve all these problems.

Experimental design refers to how participants are allocated to an experiment’s different conditions (or IV levels). There are three types:

1. Independent measures / between-groups : Different participants are used in each condition of the independent variable.

2. Repeated measures /within groups : The same participants take part in each condition of the independent variable.

3. Matched pairs : Each condition uses different participants, but they are matched in terms of important characteristics, e.g., gender, age, intelligence, etc.

Learning Check

Read about each of the experiments below. For each experiment, identify (1) which experimental design was used; and (2) why the researcher might have used that design.

1 . To compare the effectiveness of two different types of therapy for depression, depressed patients were assigned to receive either cognitive therapy or behavior therapy for a 12-week period.

The researchers attempted to ensure that the patients in the two groups had similar severity of depressed symptoms by administering a standardized test of depression to each participant, then pairing them according to the severity of their symptoms.

2 . To assess the difference in reading comprehension between 7 and 9-year-olds, a researcher recruited each group from a local primary school. They were given the same passage of text to read and then asked a series of questions to assess their understanding.

3 . To assess the effectiveness of two different ways of teaching reading, a group of 5-year-olds was recruited from a primary school. Their level of reading ability was assessed, and then they were taught using scheme one for 20 weeks.

At the end of this period, their reading was reassessed, and a reading improvement score was calculated. They were then taught using scheme two for a further 20 weeks, and another reading improvement score for this period was calculated. The reading improvement scores for each child were then compared.

4 . To assess the effect of the organization on recall, a researcher randomly assigned student volunteers to two conditions.

Condition one attempted to recall a list of words that were organized into meaningful categories; condition two attempted to recall the same words, randomly grouped on the page.

Experiment Terminology

Ecological validity.

The degree to which an investigation represents real-life experiences.

Experimenter effects

These are the ways that the experimenter can accidentally influence the participant through their appearance or behavior.

Demand characteristics

The clues in an experiment lead the participants to think they know what the researcher is looking for (e.g., the experimenter’s body language).

Independent variable (IV)

The variable the experimenter manipulates (i.e., changes) is assumed to have a direct effect on the dependent variable.

Dependent variable (DV)

Variable the experimenter measures. This is the outcome (i.e., the result) of a study.

Extraneous variables (EV)

All variables which are not independent variables but could affect the results (DV) of the experiment. Extraneous variables should be controlled where possible.

Confounding variables

Variable(s) that have affected the results (DV), apart from the IV. A confounding variable could be an extraneous variable that has not been controlled.

Random Allocation

Randomly allocating participants to independent variable conditions means that all participants should have an equal chance of taking part in each condition.

The principle of random allocation is to avoid bias in how the experiment is carried out and limit the effects of participant variables.

Order effects

Changes in participants’ performance due to their repeating the same or similar test more than once. Examples of order effects include:

(i) practice effect: an improvement in performance on a task due to repetition, for example, because of familiarity with the task;

(ii) fatigue effect: a decrease in performance of a task due to repetition, for example, because of boredom or tiredness.

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Experimental Design – Types, Methods, Guide

Table of Contents

Experimental Design

Experimental design is a process of planning and conducting scientific experiments to investigate a hypothesis or research question. It involves carefully designing an experiment that can test the hypothesis, and controlling for other variables that may influence the results.

Experimental design typically includes identifying the variables that will be manipulated or measured, defining the sample or population to be studied, selecting an appropriate method of sampling, choosing a method for data collection and analysis, and determining the appropriate statistical tests to use.

Types of Experimental Design

Here are the different types of experimental design:

Completely Randomized Design

In this design, participants are randomly assigned to one of two or more groups, and each group is exposed to a different treatment or condition.

Randomized Block Design

This design involves dividing participants into blocks based on a specific characteristic, such as age or gender, and then randomly assigning participants within each block to one of two or more treatment groups.

Factorial Design

In a factorial design, participants are randomly assigned to one of several groups, each of which receives a different combination of two or more independent variables.

Repeated Measures Design

In this design, each participant is exposed to all of the different treatments or conditions, either in a random order or in a predetermined order.

Crossover Design

This design involves randomly assigning participants to one of two or more treatment groups, with each group receiving one treatment during the first phase of the study and then switching to a different treatment during the second phase.

Split-plot Design

In this design, the researcher manipulates one or more variables at different levels and uses a randomized block design to control for other variables.

Nested Design

This design involves grouping participants within larger units, such as schools or households, and then randomly assigning these units to different treatment groups.

Laboratory Experiment

Laboratory experiments are conducted under controlled conditions, which allows for greater precision and accuracy. However, because laboratory conditions are not always representative of real-world conditions, the results of these experiments may not be generalizable to the population at large.

Field Experiment

Field experiments are conducted in naturalistic settings and allow for more realistic observations. However, because field experiments are not as controlled as laboratory experiments, they may be subject to more sources of error.

Experimental Design Methods

Experimental design methods refer to the techniques and procedures used to design and conduct experiments in scientific research. Here are some common experimental design methods:

Randomization

This involves randomly assigning participants to different groups or treatments to ensure that any observed differences between groups are due to the treatment and not to other factors.

Control Group

The use of a control group is an important experimental design method that involves having a group of participants that do not receive the treatment or intervention being studied. The control group is used as a baseline to compare the effects of the treatment group.

Blinding involves keeping participants, researchers, or both unaware of which treatment group participants are in, in order to reduce the risk of bias in the results.

Counterbalancing

This involves systematically varying the order in which participants receive treatments or interventions in order to control for order effects.

Replication

Replication involves conducting the same experiment with different samples or under different conditions to increase the reliability and validity of the results.

This experimental design method involves manipulating multiple independent variables simultaneously to investigate their combined effects on the dependent variable.

This involves dividing participants into subgroups or blocks based on specific characteristics, such as age or gender, in order to reduce the risk of confounding variables.

Data Collection Method

Experimental design data collection methods are techniques and procedures used to collect data in experimental research. Here are some common experimental design data collection methods:

Direct Observation

This method involves observing and recording the behavior or phenomenon of interest in real time. It may involve the use of structured or unstructured observation, and may be conducted in a laboratory or naturalistic setting.

Self-report Measures

Self-report measures involve asking participants to report their thoughts, feelings, or behaviors using questionnaires, surveys, or interviews. These measures may be administered in person or online.

Behavioral Measures

Behavioral measures involve measuring participants’ behavior directly, such as through reaction time tasks or performance tests. These measures may be administered using specialized equipment or software.

Physiological Measures

Physiological measures involve measuring participants’ physiological responses, such as heart rate, blood pressure, or brain activity, using specialized equipment. These measures may be invasive or non-invasive, and may be administered in a laboratory or clinical setting.

Archival Data

Archival data involves using existing records or data, such as medical records, administrative records, or historical documents, as a source of information. These data may be collected from public or private sources.

Computerized Measures

Computerized measures involve using software or computer programs to collect data on participants’ behavior or responses. These measures may include reaction time tasks, cognitive tests, or other types of computer-based assessments.

Video Recording

Video recording involves recording participants’ behavior or interactions using cameras or other recording equipment. This method can be used to capture detailed information about participants’ behavior or to analyze social interactions.

Data Analysis Method

Experimental design data analysis methods refer to the statistical techniques and procedures used to analyze data collected in experimental research. Here are some common experimental design data analysis methods:

Descriptive Statistics

Descriptive statistics are used to summarize and describe the data collected in the study. This includes measures such as mean, median, mode, range, and standard deviation.

Inferential Statistics

Inferential statistics are used to make inferences or generalizations about a larger population based on the data collected in the study. This includes hypothesis testing and estimation.

Analysis of Variance (ANOVA)

ANOVA is a statistical technique used to compare means across two or more groups in order to determine whether there are significant differences between the groups. There are several types of ANOVA, including one-way ANOVA, two-way ANOVA, and repeated measures ANOVA.

Regression Analysis

Regression analysis is used to model the relationship between two or more variables in order to determine the strength and direction of the relationship. There are several types of regression analysis, including linear regression, logistic regression, and multiple regression.

Factor Analysis

Factor analysis is used to identify underlying factors or dimensions in a set of variables. This can be used to reduce the complexity of the data and identify patterns in the data.

Structural Equation Modeling (SEM)

SEM is a statistical technique used to model complex relationships between variables. It can be used to test complex theories and models of causality.

Cluster Analysis

Cluster analysis is used to group similar cases or observations together based on similarities or differences in their characteristics.

Time Series Analysis

Time series analysis is used to analyze data collected over time in order to identify trends, patterns, or changes in the data.

Multilevel Modeling

Multilevel modeling is used to analyze data that is nested within multiple levels, such as students nested within schools or employees nested within companies.

Applications of Experimental Design 

Experimental design is a versatile research methodology that can be applied in many fields. Here are some applications of experimental design:

• Medical Research: Experimental design is commonly used to test new treatments or medications for various medical conditions. This includes clinical trials to evaluate the safety and effectiveness of new drugs or medical devices.
• Agriculture : Experimental design is used to test new crop varieties, fertilizers, and other agricultural practices. This includes randomized field trials to evaluate the effects of different treatments on crop yield, quality, and pest resistance.
• Environmental science: Experimental design is used to study the effects of environmental factors, such as pollution or climate change, on ecosystems and wildlife. This includes controlled experiments to study the effects of pollutants on plant growth or animal behavior.
• Psychology : Experimental design is used to study human behavior and cognitive processes. This includes experiments to test the effects of different interventions, such as therapy or medication, on mental health outcomes.
• Engineering : Experimental design is used to test new materials, designs, and manufacturing processes in engineering applications. This includes laboratory experiments to test the strength and durability of new materials, or field experiments to test the performance of new technologies.
• Education : Experimental design is used to evaluate the effectiveness of teaching methods, educational interventions, and programs. This includes randomized controlled trials to compare different teaching methods or evaluate the impact of educational programs on student outcomes.
• Marketing : Experimental design is used to test the effectiveness of marketing campaigns, pricing strategies, and product designs. This includes experiments to test the impact of different marketing messages or pricing schemes on consumer behavior.

Examples of Experimental Design 

Here are some examples of experimental design in different fields:

• Example in Medical research : A study that investigates the effectiveness of a new drug treatment for a particular condition. Patients are randomly assigned to either a treatment group or a control group, with the treatment group receiving the new drug and the control group receiving a placebo. The outcomes, such as improvement in symptoms or side effects, are measured and compared between the two groups.
• Example in Education research: A study that examines the impact of a new teaching method on student learning outcomes. Students are randomly assigned to either a group that receives the new teaching method or a group that receives the traditional teaching method. Student achievement is measured before and after the intervention, and the results are compared between the two groups.
• Example in Environmental science: A study that tests the effectiveness of a new method for reducing pollution in a river. Two sections of the river are selected, with one section treated with the new method and the other section left untreated. The water quality is measured before and after the intervention, and the results are compared between the two sections.
• Example in Marketing research: A study that investigates the impact of a new advertising campaign on consumer behavior. Participants are randomly assigned to either a group that is exposed to the new campaign or a group that is not. Their behavior, such as purchasing or product awareness, is measured and compared between the two groups.
• Example in Social psychology: A study that examines the effect of a new social intervention on reducing prejudice towards a marginalized group. Participants are randomly assigned to either a group that receives the intervention or a control group that does not. Their attitudes and behavior towards the marginalized group are measured before and after the intervention, and the results are compared between the two groups.

When to use Experimental Research Design 

Experimental research design should be used when a researcher wants to establish a cause-and-effect relationship between variables. It is particularly useful when studying the impact of an intervention or treatment on a particular outcome.

Here are some situations where experimental research design may be appropriate:

• When studying the effects of a new drug or medical treatment: Experimental research design is commonly used in medical research to test the effectiveness and safety of new drugs or medical treatments. By randomly assigning patients to treatment and control groups, researchers can determine whether the treatment is effective in improving health outcomes.
• When evaluating the effectiveness of an educational intervention: An experimental research design can be used to evaluate the impact of a new teaching method or educational program on student learning outcomes. By randomly assigning students to treatment and control groups, researchers can determine whether the intervention is effective in improving academic performance.
• When testing the effectiveness of a marketing campaign: An experimental research design can be used to test the effectiveness of different marketing messages or strategies. By randomly assigning participants to treatment and control groups, researchers can determine whether the marketing campaign is effective in changing consumer behavior.
• When studying the effects of an environmental intervention: Experimental research design can be used to study the impact of environmental interventions, such as pollution reduction programs or conservation efforts. By randomly assigning locations or areas to treatment and control groups, researchers can determine whether the intervention is effective in improving environmental outcomes.
• When testing the effects of a new technology: An experimental research design can be used to test the effectiveness and safety of new technologies or engineering designs. By randomly assigning participants or locations to treatment and control groups, researchers can determine whether the new technology is effective in achieving its intended purpose.

How to Conduct Experimental Research

Here are the steps to conduct Experimental Research:

• Identify a Research Question : Start by identifying a research question that you want to answer through the experiment. The question should be clear, specific, and testable.
• Develop a Hypothesis: Based on your research question, develop a hypothesis that predicts the relationship between the independent and dependent variables. The hypothesis should be clear and testable.
• Design the Experiment : Determine the type of experimental design you will use, such as a between-subjects design or a within-subjects design. Also, decide on the experimental conditions, such as the number of independent variables, the levels of the independent variable, and the dependent variable to be measured.
• Select Participants: Select the participants who will take part in the experiment. They should be representative of the population you are interested in studying.
• Randomly Assign Participants to Groups: If you are using a between-subjects design, randomly assign participants to groups to control for individual differences.
• Conduct the Experiment : Conduct the experiment by manipulating the independent variable(s) and measuring the dependent variable(s) across the different conditions.
• Analyze the Data: Analyze the data using appropriate statistical methods to determine if there is a significant effect of the independent variable(s) on the dependent variable(s).
• Draw Conclusions: Based on the data analysis, draw conclusions about the relationship between the independent and dependent variables. If the results support the hypothesis, then it is accepted. If the results do not support the hypothesis, then it is rejected.
• Communicate the Results: Finally, communicate the results of the experiment through a research report or presentation. Include the purpose of the study, the methods used, the results obtained, and the conclusions drawn.

Purpose of Experimental Design 

The purpose of experimental design is to control and manipulate one or more independent variables to determine their effect on a dependent variable. Experimental design allows researchers to systematically investigate causal relationships between variables, and to establish cause-and-effect relationships between the independent and dependent variables. Through experimental design, researchers can test hypotheses and make inferences about the population from which the sample was drawn.

Experimental design provides a structured approach to designing and conducting experiments, ensuring that the results are reliable and valid. By carefully controlling for extraneous variables that may affect the outcome of the study, experimental design allows researchers to isolate the effect of the independent variable(s) on the dependent variable(s), and to minimize the influence of other factors that may confound the results.

Experimental design also allows researchers to generalize their findings to the larger population from which the sample was drawn. By randomly selecting participants and using statistical techniques to analyze the data, researchers can make inferences about the larger population with a high degree of confidence.

Overall, the purpose of experimental design is to provide a rigorous, systematic, and scientific method for testing hypotheses and establishing cause-and-effect relationships between variables. Experimental design is a powerful tool for advancing scientific knowledge and informing evidence-based practice in various fields, including psychology, biology, medicine, engineering, and social sciences.

Advantages of Experimental Design 

Experimental design offers several advantages in research. Here are some of the main advantages:

• Control over extraneous variables: Experimental design allows researchers to control for extraneous variables that may affect the outcome of the study. By manipulating the independent variable and holding all other variables constant, researchers can isolate the effect of the independent variable on the dependent variable.
• Establishing causality: Experimental design allows researchers to establish causality by manipulating the independent variable and observing its effect on the dependent variable. This allows researchers to determine whether changes in the independent variable cause changes in the dependent variable.
• Replication : Experimental design allows researchers to replicate their experiments to ensure that the findings are consistent and reliable. Replication is important for establishing the validity and generalizability of the findings.
• Random assignment: Experimental design often involves randomly assigning participants to conditions. This helps to ensure that individual differences between participants are evenly distributed across conditions, which increases the internal validity of the study.
• Precision : Experimental design allows researchers to measure variables with precision, which can increase the accuracy and reliability of the data.
• Generalizability : If the study is well-designed, experimental design can increase the generalizability of the findings. By controlling for extraneous variables and using random assignment, researchers can increase the likelihood that the findings will apply to other populations and contexts.

Limitations of Experimental Design

Experimental design has some limitations that researchers should be aware of. Here are some of the main limitations:

• Artificiality : Experimental design often involves creating artificial situations that may not reflect real-world situations. This can limit the external validity of the findings, or the extent to which the findings can be generalized to real-world settings.
• Ethical concerns: Some experimental designs may raise ethical concerns, particularly if they involve manipulating variables that could cause harm to participants or if they involve deception.
• Participant bias : Participants in experimental studies may modify their behavior in response to the experiment, which can lead to participant bias.
• Limited generalizability: The conditions of the experiment may not reflect the complexities of real-world situations. As a result, the findings may not be applicable to all populations and contexts.
• Cost and time : Experimental design can be expensive and time-consuming, particularly if the experiment requires specialized equipment or if the sample size is large.
• Researcher bias : Researchers may unintentionally bias the results of the experiment if they have expectations or preferences for certain outcomes.
• Lack of feasibility : Experimental design may not be feasible in some cases, particularly if the research question involves variables that cannot be manipulated or controlled.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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Keyboard Shortcuts

1.1 - a quick history of the design of experiments (doe).

The textbook we are using brings an engineering perspective to the design of experiments. We will bring in other contexts and examples from other fields of study including agriculture (where much of the early research was done) education and nutrition. Surprisingly the service industry has begun using design of experiments as well.

  All experiments are designed experiments, it is just that some are poorly designed and some are well-designed.  

Engineering Experiments Section  

If we had infinite time and resource budgets there probably wouldn't be a big fuss made over designing experiments. In production and quality control we want to control the error and learn as much as we can about the process or the underlying theory with the resources at hand. From an engineering perspective we're trying to use experimentation for the following purposes:

• reduce time to design/develop new products & processes
• improve performance of existing processes
• improve reliability and performance of products
• achieve product & process robustness
• perform evaluation of materials, design alternatives, setting component & system tolerances, etc.

We always want to fine-tune or improve the process. In today's global world this drive for competitiveness affects all of us both as consumers and producers.

Robustness is a concept that enters into statistics at several points. At the analysis, stage robustness refers to a technique that isn't overly influenced by bad data. Even if there is an outlier or bad data you still want to get the right answer. Regardless of who or what is involved in the process - it is still going to work. We will come back to this notion of robustness later in the course (Lesson 12).

Every experiment design has inputs. Back to the cake baking example: we have our ingredients such as flour, sugar, milk, eggs, etc. Regardless of the quality of these ingredients we still want our cake to come out successfully. In every experiment there are inputs and in addition, there are factors (such as time of baking, temperature, geometry of the cake pan, etc.), some of which you can control and others that you can't control. The experimenter must think about factors that affect the outcome. We also talk about the output and the yield or the response to your experiment. For the cake, the output might be measured as texture, flavor, height, size, or flavor.

Four Eras in the History of DOE Section  

Here's a quick timeline:

• R. A. Fisher & his co-workers
• Profound impact on agricultural science
• Factorial designs, ANOVA
• Box & Wilson, response surfaces
• Applications in the chemical & process industries
• Quality improvement initiatives in many companies
• CQI and TQM were important ideas and became management goals
• Taguchi and robust parameter design, process robustness
• The modern era, beginning circa 1990, when economic competitiveness and globalization are driving all sectors of the economy to be more competitive.

Immediately following World War II the first industrial era marked another resurgence in the use of DOE. It was at this time that Box and Wilson (1951) wrote the key paper in response surface designs thinking of the output as a response function and trying to find the optimum conditions for this function. George Box died early in 2013. And, an interesting fact here - he married Fisher's daughter! He worked in the chemical industry in England in his early career and then came to America and worked at the University of Wisconsin for most of his career.

The Second Industrial Era - or the Quality Revolution

W. Edwards Deming

The importance of statistical quality control was taken to Japan in the 1950s by W Edward Deming. This started what Montgomery calls a second Industrial Era, and sometimes the quality revolution. After the second world war, Japanese products were of terrible quality. They were cheaply made and not very good. In the 1960s their quality started improving. The Japanese car industry adopted statistical quality control procedures and conducted experiments which started this new era. Total Quality Management (TQM), Continuous Quality Improvement (CQI) are management techniques that have come out of this statistical quality revolution - statistical quality control and design of experiments.

Taguchi, a Japanese engineer, discovered and published a lot of the techniques that were later brought to the West, using an independent development of what he referred to as orthogonal arrays. In the West, these were referred to as fractional factorial designs. These are both very similar and we will discuss both of these in this course. He came up with the concept of robust parameter design and process robustness.

The Modern Era

Around 1990 Six Sigma, a new way of representing CQI, became popular. Now it is a company and they employ a technique which has been adopted by many of the large manufacturing companies. This is a technique that uses statistics to make decisions based on quality and feedback loops. It incorporates a lot of previous statistical and management techniques.

Clinical Trials

Montgomery omits in this brief history a major part of design of experimentation that evolved - clinical trials. This evolved in the 1960s when medical advances were previously based on anecdotal data; a doctor would examine six patients and from this wrote a paper and published it. The incredible biases resulting from these kinds of anecdotal studies became known. The outcome was a move toward making the randomized double-blind clinical trial the gold standard for approval of any new product, medical device, or procedure. The scientific application of the statistical procedures became very important.

19+ Experimental Design Examples (Methods + Types)

Ever wondered how scientists discover new medicines, psychologists learn about behavior, or even how marketers figure out what kind of ads you like? Well, they all have something in common: they use a special plan or recipe called an "experimental design."

Imagine you're baking cookies. You can't just throw random amounts of flour, sugar, and chocolate chips into a bowl and hope for the best. You follow a recipe, right? Scientists and researchers do something similar. They follow a "recipe" called an experimental design to make sure their experiments are set up in a way that the answers they find are meaningful and reliable.

Experimental design is the roadmap researchers use to answer questions. It's a set of rules and steps that researchers follow to collect information, or "data," in a way that is fair, accurate, and makes sense.

Long ago, people didn't have detailed game plans for experiments. They often just tried things out and saw what happened. But over time, people got smarter about this. They started creating structured plans—what we now call experimental designs—to get clearer, more trustworthy answers to their questions.

In this article, we'll take you on a journey through the world of experimental designs. We'll talk about the different types, or "flavors," of experimental designs, where they're used, and even give you a peek into how they came to be.

What Is Experimental Design?

Alright, before we dive into the different types of experimental designs, let's get crystal clear on what experimental design actually is.

Imagine you're a detective trying to solve a mystery. You need clues, right? Well, in the world of research, experimental design is like the roadmap that helps you find those clues. It's like the game plan in sports or the blueprint when you're building a house. Just like you wouldn't start building without a good blueprint, researchers won't start their studies without a strong experimental design.

So, why do we need experimental design? Think about baking a cake. If you toss ingredients into a bowl without measuring, you'll end up with a mess instead of a tasty dessert.

Similarly, in research, if you don't have a solid plan, you might get confusing or incorrect results. A good experimental design helps you ask the right questions ( think critically ), decide what to measure ( come up with an idea ), and figure out how to measure it (test it). It also helps you consider things that might mess up your results, like outside influences you hadn't thought of.

For example, let's say you want to find out if listening to music helps people focus better. Your experimental design would help you decide things like: Who are you going to test? What kind of music will you use? How will you measure focus? And, importantly, how will you make sure that it's really the music affecting focus and not something else, like the time of day or whether someone had a good breakfast?

In short, experimental design is the master plan that guides researchers through the process of collecting data, so they can answer questions in the most reliable way possible. It's like the GPS for the journey of discovery!

History of Experimental Design

Around 350 BCE, people like Aristotle were trying to figure out how the world works, but they mostly just thought really hard about things. They didn't test their ideas much. So while they were super smart, their methods weren't always the best for finding out the truth.

Fast forward to the Renaissance (14th to 17th centuries), a time of big changes and lots of curiosity. People like Galileo started to experiment by actually doing tests, like rolling balls down inclined planes to study motion. Galileo's work was cool because he combined thinking with doing. He'd have an idea, test it, look at the results, and then think some more. This approach was a lot more reliable than just sitting around and thinking.

Now, let's zoom ahead to the 18th and 19th centuries. This is when people like Francis Galton, an English polymath, started to get really systematic about experimentation. Galton was obsessed with measuring things. Seriously, he even tried to measure how good-looking people were ! His work helped create the foundations for a more organized approach to experiments.

Next stop: the early 20th century. Enter Ronald A. Fisher , a brilliant British statistician. Fisher was a game-changer. He came up with ideas that are like the bread and butter of modern experimental design.

Fisher invented the concept of the " control group "—that's a group of people or things that don't get the treatment you're testing, so you can compare them to those who do. He also stressed the importance of " randomization ," which means assigning people or things to different groups by chance, like drawing names out of a hat. This makes sure the experiment is fair and the results are trustworthy.

Around the same time, American psychologists like John B. Watson and B.F. Skinner were developing " behaviorism ." They focused on studying things that they could directly observe and measure, like actions and reactions.

Skinner even built boxes—called Skinner Boxes —to test how animals like pigeons and rats learn. Their work helped shape how psychologists design experiments today. Watson performed a very controversial experiment called The Little Albert experiment that helped describe behaviour through conditioning—in other words, how people learn to behave the way they do.

In the later part of the 20th century and into our time, computers have totally shaken things up. Researchers now use super powerful software to help design their experiments and crunch the numbers.

With computers, they can simulate complex experiments before they even start, which helps them predict what might happen. This is especially helpful in fields like medicine, where getting things right can be a matter of life and death.

Also, did you know that experimental designs aren't just for scientists in labs? They're used by people in all sorts of jobs, like marketing, education, and even video game design! Yes, someone probably ran an experiment to figure out what makes a game super fun to play.

So there you have it—a quick tour through the history of experimental design, from Aristotle's deep thoughts to Fisher's groundbreaking ideas, and all the way to today's computer-powered research. These designs are the recipes that help people from all walks of life find answers to their big questions.

Key Terms in Experimental Design

Before we dig into the different types of experimental designs, let's get comfy with some key terms. Understanding these terms will make it easier for us to explore the various types of experimental designs that researchers use to answer their big questions.

Independent Variable : This is what you change or control in your experiment to see what effect it has. Think of it as the "cause" in a cause-and-effect relationship. For example, if you're studying whether different types of music help people focus, the kind of music is the independent variable.

Dependent Variable : This is what you're measuring to see the effect of your independent variable. In our music and focus experiment, how well people focus is the dependent variable—it's what "depends" on the kind of music played.

Control Group : This is a group of people who don't get the special treatment or change you're testing. They help you see what happens when the independent variable is not applied. If you're testing whether a new medicine works, the control group would take a fake pill, called a placebo , instead of the real medicine.

Experimental Group : This is the group that gets the special treatment or change you're interested in. Going back to our medicine example, this group would get the actual medicine to see if it has any effect.

Randomization : This is like shaking things up in a fair way. You randomly put people into the control or experimental group so that each group is a good mix of different kinds of people. This helps make the results more reliable.

Sample : This is the group of people you're studying. They're a "sample" of a larger group that you're interested in. For instance, if you want to know how teenagers feel about a new video game, you might study a sample of 100 teenagers.

Bias : This is anything that might tilt your experiment one way or another without you realizing it. Like if you're testing a new kind of dog food and you only test it on poodles, that could create a bias because maybe poodles just really like that food and other breeds don't.

Data : This is the information you collect during the experiment. It's like the treasure you find on your journey of discovery!

Replication : This means doing the experiment more than once to make sure your findings hold up. It's like double-checking your answers on a test.

Hypothesis : This is your educated guess about what will happen in the experiment. It's like predicting the end of a movie based on the first half.

Steps of Experimental Design

Alright, let's say you're all fired up and ready to run your own experiment. Cool! But where do you start? Well, designing an experiment is a bit like planning a road trip. There are some key steps you've got to take to make sure you reach your destination. Let's break it down:

• Ask a Question : Before you hit the road, you've got to know where you're going. Same with experiments. You start with a question you want to answer, like "Does eating breakfast really make you do better in school?"
• Do Some Homework : Before you pack your bags, you look up the best places to visit, right? In science, this means reading up on what other people have already discovered about your topic.
• Form a Hypothesis : This is your educated guess about what you think will happen. It's like saying, "I bet this route will get us there faster."
• Plan the Details : Now you decide what kind of car you're driving (your experimental design), who's coming with you (your sample), and what snacks to bring (your variables).
• Randomization : Remember, this is like shuffling a deck of cards. You want to mix up who goes into your control and experimental groups to make sure it's a fair test.
• Run the Experiment : Finally, the rubber hits the road! You carry out your plan, making sure to collect your data carefully.
• Analyze the Data : Once the trip's over, you look at your photos and decide which ones are keepers. In science, this means looking at your data to see what it tells you.
• Draw Conclusions : Based on your data, did you find an answer to your question? This is like saying, "Yep, that route was faster," or "Nope, we hit a ton of traffic."
• Share Your Findings : After a great trip, you want to tell everyone about it, right? Scientists do the same by publishing their results so others can learn from them.
• Do It Again? : Sometimes one road trip just isn't enough. In the same way, scientists often repeat their experiments to make sure their findings are solid.

So there you have it! Those are the basic steps you need to follow when you're designing an experiment. Each step helps make sure that you're setting up a fair and reliable way to find answers to your big questions.

Let's get into examples of experimental designs.

1) True Experimental Design

In the world of experiments, the True Experimental Design is like the superstar quarterback everyone talks about. Born out of the early 20th-century work of statisticians like Ronald A. Fisher, this design is all about control, precision, and reliability.

Researchers carefully pick an independent variable to manipulate (remember, that's the thing they're changing on purpose) and measure the dependent variable (the effect they're studying). Then comes the magic trick—randomization. By randomly putting participants into either the control or experimental group, scientists make sure their experiment is as fair as possible.

No sneaky biases here!

True Experimental Design Pros

The pros of True Experimental Design are like the perks of a VIP ticket at a concert: you get the best and most trustworthy results. Because everything is controlled and randomized, you can feel pretty confident that the results aren't just a fluke.

True Experimental Design Cons

However, there's a catch. Sometimes, it's really tough to set up these experiments in a real-world situation. Imagine trying to control every single detail of your day, from the food you eat to the air you breathe. Not so easy, right?

True Experimental Design Uses

The fields that get the most out of True Experimental Designs are those that need super reliable results, like medical research.

When scientists were developing COVID-19 vaccines, they used this design to run clinical trials. They had control groups that received a placebo (a harmless substance with no effect) and experimental groups that got the actual vaccine. Then they measured how many people in each group got sick. By comparing the two, they could say, "Yep, this vaccine works!"

So next time you read about a groundbreaking discovery in medicine or technology, chances are a True Experimental Design was the VIP behind the scenes, making sure everything was on point. It's been the go-to for rigorous scientific inquiry for nearly a century, and it's not stepping off the stage anytime soon.

2) Quasi-Experimental Design

So, let's talk about the Quasi-Experimental Design. Think of this one as the cool cousin of True Experimental Design. It wants to be just like its famous relative, but it's a bit more laid-back and flexible. You'll find quasi-experimental designs when it's tricky to set up a full-blown True Experimental Design with all the bells and whistles.

Quasi-experiments still play with an independent variable, just like their stricter cousins. The big difference? They don't use randomization. It's like wanting to divide a bag of jelly beans equally between your friends, but you can't quite do it perfectly.

In real life, it's often not possible or ethical to randomly assign people to different groups, especially when dealing with sensitive topics like education or social issues. And that's where quasi-experiments come in.

Quasi-Experimental Design Pros

Even though they lack full randomization, quasi-experimental designs are like the Swiss Army knives of research: versatile and practical. They're especially popular in fields like education, sociology, and public policy.

For instance, when researchers wanted to figure out if the Head Start program , aimed at giving young kids a "head start" in school, was effective, they used a quasi-experimental design. They couldn't randomly assign kids to go or not go to preschool, but they could compare kids who did with kids who didn't.

Quasi-Experimental Design Cons

Of course, quasi-experiments come with their own bag of pros and cons. On the plus side, they're easier to set up and often cheaper than true experiments. But the flip side is that they're not as rock-solid in their conclusions. Because the groups aren't randomly assigned, there's always that little voice saying, "Hey, are we missing something here?"

Quasi-Experimental Design Uses

Quasi-Experimental Design gained traction in the mid-20th century. Researchers were grappling with real-world problems that didn't fit neatly into a laboratory setting. Plus, as society became more aware of ethical considerations, the need for flexible designs increased. So, the quasi-experimental approach was like a breath of fresh air for scientists wanting to study complex issues without a laundry list of restrictions.

In short, if True Experimental Design is the superstar quarterback, Quasi-Experimental Design is the versatile player who can adapt and still make significant contributions to the game.

3) Pre-Experimental Design

Now, let's talk about the Pre-Experimental Design. Imagine it as the beginner's skateboard you get before you try out for all the cool tricks. It has wheels, it rolls, but it's not built for the professional skatepark.

Similarly, pre-experimental designs give researchers a starting point. They let you dip your toes in the water of scientific research without diving in head-first.

So, what's the deal with pre-experimental designs?

Pre-Experimental Designs are the basic, no-frills versions of experiments. Researchers still mess around with an independent variable and measure a dependent variable, but they skip over the whole randomization thing and often don't even have a control group.

It's like baking a cake but forgetting the frosting and sprinkles; you'll get some results, but they might not be as complete or reliable as you'd like.

Pre-Experimental Design Pros

Why use such a simple setup? Because sometimes, you just need to get the ball rolling. Pre-experimental designs are great for quick-and-dirty research when you're short on time or resources. They give you a rough idea of what's happening, which you can use to plan more detailed studies later.

A good example of this is early studies on the effects of screen time on kids. Researchers couldn't control every aspect of a child's life, but they could easily ask parents to track how much time their kids spent in front of screens and then look for trends in behavior or school performance.

Pre-Experimental Design Cons

But here's the catch: pre-experimental designs are like that first draft of an essay. It helps you get your ideas down, but you wouldn't want to turn it in for a grade. Because these designs lack the rigorous structure of true or quasi-experimental setups, they can't give you rock-solid conclusions. They're more like clues or signposts pointing you in a certain direction.

Pre-Experimental Design Uses

This type of design became popular in the early stages of various scientific fields. Researchers used them to scratch the surface of a topic, generate some initial data, and then decide if it's worth exploring further. In other words, pre-experimental designs were the stepping stones that led to more complex, thorough investigations.

So, while Pre-Experimental Design may not be the star player on the team, it's like the practice squad that helps everyone get better. It's the starting point that can lead to bigger and better things.

4) Factorial Design

Now, buckle up, because we're moving into the world of Factorial Design, the multi-tasker of the experimental universe.

Imagine juggling not just one, but multiple balls in the air—that's what researchers do in a factorial design.

In Factorial Design, researchers are not satisfied with just studying one independent variable. Nope, they want to study two or more at the same time to see how they interact.

It's like cooking with several spices to see how they blend together to create unique flavors.

Factorial Design became the talk of the town with the rise of computers. Why? Because this design produces a lot of data, and computers are the number crunchers that help make sense of it all. So, thanks to our silicon friends, researchers can study complicated questions like, "How do diet AND exercise together affect weight loss?" instead of looking at just one of those factors.

Factorial Design Pros

This design's main selling point is its ability to explore interactions between variables. For instance, maybe a new study drug works really well for young people but not so great for older adults. A factorial design could reveal that age is a crucial factor, something you might miss if you only studied the drug's effectiveness in general. It's like being a detective who looks for clues not just in one room but throughout the entire house.

Factorial Design Cons

However, factorial designs have their own bag of challenges. First off, they can be pretty complicated to set up and run. Imagine coordinating a four-way intersection with lots of cars coming from all directions—you've got to make sure everything runs smoothly, or you'll end up with a traffic jam. Similarly, researchers need to carefully plan how they'll measure and analyze all the different variables.

Factorial Design Uses

Factorial designs are widely used in psychology to untangle the web of factors that influence human behavior. They're also popular in fields like marketing, where companies want to understand how different aspects like price, packaging, and advertising influence a product's success.

And speaking of success, the factorial design has been a hit since statisticians like Ronald A. Fisher (yep, him again!) expanded on it in the early-to-mid 20th century. It offered a more nuanced way of understanding the world, proving that sometimes, to get the full picture, you've got to juggle more than one ball at a time.

So, if True Experimental Design is the quarterback and Quasi-Experimental Design is the versatile player, Factorial Design is the strategist who sees the entire game board and makes moves accordingly.

5) Longitudinal Design

Alright, let's take a step into the world of Longitudinal Design. Picture it as the grand storyteller, the kind who doesn't just tell you about a single event but spins an epic tale that stretches over years or even decades. This design isn't about quick snapshots; it's about capturing the whole movie of someone's life or a long-running process.

You know how you might take a photo every year on your birthday to see how you've changed? Longitudinal Design is kind of like that, but for scientific research.

With Longitudinal Design, instead of measuring something just once, researchers come back again and again, sometimes over many years, to see how things are going. This helps them understand not just what's happening, but why it's happening and how it changes over time.

This design really started to shine in the latter half of the 20th century, when researchers began to realize that some questions can't be answered in a hurry. Think about studies that look at how kids grow up, or research on how a certain medicine affects you over a long period. These aren't things you can rush.

The famous Framingham Heart Study , started in 1948, is a prime example. It's been studying heart health in a small town in Massachusetts for decades, and the findings have shaped what we know about heart disease.

Longitudinal Design Pros

So, what's to love about Longitudinal Design? First off, it's the go-to for studying change over time, whether that's how people age or how a forest recovers from a fire.

Longitudinal Design Cons

But it's not all sunshine and rainbows. Longitudinal studies take a lot of patience and resources. Plus, keeping track of participants over many years can be like herding cats—difficult and full of surprises.

Longitudinal Design Uses

Despite these challenges, longitudinal studies have been key in fields like psychology, sociology, and medicine. They provide the kind of deep, long-term insights that other designs just can't match.

So, if the True Experimental Design is the superstar quarterback, and the Quasi-Experimental Design is the flexible athlete, then the Factorial Design is the strategist, and the Longitudinal Design is the wise elder who has seen it all and has stories to tell.

6) Cross-Sectional Design

Now, let's flip the script and talk about Cross-Sectional Design, the polar opposite of the Longitudinal Design. If Longitudinal is the grand storyteller, think of Cross-Sectional as the snapshot photographer. It captures a single moment in time, like a selfie that you take to remember a fun day. Researchers using this design collect all their data at one point, providing a kind of "snapshot" of whatever they're studying.

In a Cross-Sectional Design, researchers look at multiple groups all at the same time to see how they're different or similar.

This design rose to popularity in the mid-20th century, mainly because it's so quick and efficient. Imagine wanting to know how people of different ages feel about a new video game. Instead of waiting for years to see how opinions change, you could just ask people of all ages what they think right now. That's Cross-Sectional Design for you—fast and straightforward.

You'll find this type of research everywhere from marketing studies to healthcare. For instance, you might have heard about surveys asking people what they think about a new product or political issue. Those are usually cross-sectional studies, aimed at getting a quick read on public opinion.

Cross-Sectional Design Pros

So, what's the big deal with Cross-Sectional Design? Well, it's the go-to when you need answers fast and don't have the time or resources for a more complicated setup.

Cross-Sectional Design Cons

Remember, speed comes with trade-offs. While you get your results quickly, those results are stuck in time. They can't tell you how things change or why they're changing, just what's happening right now.

Cross-Sectional Design Uses

Also, because they're so quick and simple, cross-sectional studies often serve as the first step in research. They give scientists an idea of what's going on so they can decide if it's worth digging deeper. In that way, they're a bit like a movie trailer, giving you a taste of the action to see if you're interested in seeing the whole film.

So, in our lineup of experimental designs, if True Experimental Design is the superstar quarterback and Longitudinal Design is the wise elder, then Cross-Sectional Design is like the speedy running back—fast, agile, but not designed for long, drawn-out plays.

7) Correlational Design

Next on our roster is the Correlational Design, the keen observer of the experimental world. Imagine this design as the person at a party who loves people-watching. They don't interfere or get involved; they just observe and take mental notes about what's going on.

In a correlational study, researchers don't change or control anything; they simply observe and measure how two variables relate to each other.

The correlational design has roots in the early days of psychology and sociology. Pioneers like Sir Francis Galton used it to study how qualities like intelligence or height could be related within families.

This design is all about asking, "Hey, when this thing happens, does that other thing usually happen too?" For example, researchers might study whether students who have more study time get better grades or whether people who exercise more have lower stress levels.

One of the most famous correlational studies you might have heard of is the link between smoking and lung cancer. Back in the mid-20th century, researchers started noticing that people who smoked a lot also seemed to get lung cancer more often. They couldn't say smoking caused cancer—that would require a true experiment—but the strong correlation was a red flag that led to more research and eventually, health warnings.

Correlational Design Pros

This design is great at proving that two (or more) things can be related. Correlational designs can help prove that more detailed research is needed on a topic. They can help us see patterns or possible causes for things that we otherwise might not have realized.

Correlational Design Cons

But here's where you need to be careful: correlational designs can be tricky. Just because two things are related doesn't mean one causes the other. That's like saying, "Every time I wear my lucky socks, my team wins." Well, it's a fun thought, but those socks aren't really controlling the game.

Correlational Design Uses

Despite this limitation, correlational designs are popular in psychology, economics, and epidemiology, to name a few fields. They're often the first step in exploring a possible relationship between variables. Once a strong correlation is found, researchers may decide to conduct more rigorous experimental studies to examine cause and effect.

So, if the True Experimental Design is the superstar quarterback and the Longitudinal Design is the wise elder, the Factorial Design is the strategist, and the Cross-Sectional Design is the speedster, then the Correlational Design is the clever scout, identifying interesting patterns but leaving the heavy lifting of proving cause and effect to the other types of designs.

8) Meta-Analysis

Last but not least, let's talk about Meta-Analysis, the librarian of experimental designs.

If other designs are all about creating new research, Meta-Analysis is about gathering up everyone else's research, sorting it, and figuring out what it all means when you put it together.

Imagine a jigsaw puzzle where each piece is a different study. Meta-Analysis is the process of fitting all those pieces together to see the big picture.

The concept of Meta-Analysis started to take shape in the late 20th century, when computers became powerful enough to handle massive amounts of data. It was like someone handed researchers a super-powered magnifying glass, letting them examine multiple studies at the same time to find common trends or results.

You might have heard of the Cochrane Reviews in healthcare . These are big collections of meta-analyses that help doctors and policymakers figure out what treatments work best based on all the research that's been done.

For example, if ten different studies show that a certain medicine helps lower blood pressure, a meta-analysis would pull all that information together to give a more accurate answer.

Meta-Analysis Pros

The beauty of Meta-Analysis is that it can provide really strong evidence. Instead of relying on one study, you're looking at the whole landscape of research on a topic.

Meta-Analysis Cons

However, it does have some downsides. For one, Meta-Analysis is only as good as the studies it includes. If those studies are flawed, the meta-analysis will be too. It's like baking a cake: if you use bad ingredients, it doesn't matter how good your recipe is—the cake won't turn out well.

Meta-Analysis Uses

Despite these challenges, meta-analyses are highly respected and widely used in many fields like medicine, psychology, and education. They help us make sense of a world that's bursting with information by showing us the big picture drawn from many smaller snapshots.

So, in our all-star lineup, if True Experimental Design is the quarterback and Longitudinal Design is the wise elder, the Factorial Design is the strategist, the Cross-Sectional Design is the speedster, and the Correlational Design is the scout, then the Meta-Analysis is like the coach, using insights from everyone else's plays to come up with the best game plan.

9) Non-Experimental Design

Now, let's talk about a player who's a bit of an outsider on this team of experimental designs—the Non-Experimental Design. Think of this design as the commentator or the journalist who covers the game but doesn't actually play.

In a Non-Experimental Design, researchers are like reporters gathering facts, but they don't interfere or change anything. They're simply there to describe and analyze.

Non-Experimental Design Pros

So, what's the deal with Non-Experimental Design? Its strength is in description and exploration. It's really good for studying things as they are in the real world, without changing any conditions.

Non-Experimental Design Cons

Because a non-experimental design doesn't manipulate variables, it can't prove cause and effect. It's like a weather reporter: they can tell you it's raining, but they can't tell you why it's raining.

The downside? Since researchers aren't controlling variables, it's hard to rule out other explanations for what they observe. It's like hearing one side of a story—you get an idea of what happened, but it might not be the complete picture.

Non-Experimental Design Uses

Non-Experimental Design has always been a part of research, especially in fields like anthropology, sociology, and some areas of psychology.

For instance, if you've ever heard of studies that describe how people behave in different cultures or what teens like to do in their free time, that's often Non-Experimental Design at work. These studies aim to capture the essence of a situation, like painting a portrait instead of taking a snapshot.

One well-known example you might have heard about is the Kinsey Reports from the 1940s and 1950s, which described sexual behavior in men and women. Researchers interviewed thousands of people but didn't manipulate any variables like you would in a true experiment. They simply collected data to create a comprehensive picture of the subject matter.

So, in our metaphorical team of research designs, if True Experimental Design is the quarterback and Longitudinal Design is the wise elder, Factorial Design is the strategist, Cross-Sectional Design is the speedster, Correlational Design is the scout, and Meta-Analysis is the coach, then Non-Experimental Design is the sports journalist—always present, capturing the game, but not part of the action itself.

10) Repeated Measures Design

Time to meet the Repeated Measures Design, the time traveler of our research team. If this design were a player in a sports game, it would be the one who keeps revisiting past plays to figure out how to improve the next one.

Repeated Measures Design is all about studying the same people or subjects multiple times to see how they change or react under different conditions.

The idea behind Repeated Measures Design isn't new; it's been around since the early days of psychology and medicine. You could say it's a cousin to the Longitudinal Design, but instead of looking at how things naturally change over time, it focuses on how the same group reacts to different things.

Imagine a study looking at how a new energy drink affects people's running speed. Instead of comparing one group that drank the energy drink to another group that didn't, a Repeated Measures Design would have the same group of people run multiple times—once with the energy drink, and once without. This way, you're really zeroing in on the effect of that energy drink, making the results more reliable.

Repeated Measures Design Pros

The strong point of Repeated Measures Design is that it's super focused. Because it uses the same subjects, you don't have to worry about differences between groups messing up your results.

Repeated Measures Design Cons

But the downside? Well, people can get tired or bored if they're tested too many times, which might affect how they respond.

Repeated Measures Design Uses

A famous example of this design is the "Little Albert" experiment, conducted by John B. Watson and Rosalie Rayner in 1920. In this study, a young boy was exposed to a white rat and other stimuli several times to see how his emotional responses changed. Though the ethical standards of this experiment are often criticized today, it was groundbreaking in understanding conditioned emotional responses.

In our metaphorical lineup of research designs, if True Experimental Design is the quarterback and Longitudinal Design is the wise elder, Factorial Design is the strategist, Cross-Sectional Design is the speedster, Correlational Design is the scout, Meta-Analysis is the coach, and Non-Experimental Design is the journalist, then Repeated Measures Design is the time traveler—always looping back to fine-tune the game plan.

11) Crossover Design

Next up is Crossover Design, the switch-hitter of the research world. If you're familiar with baseball, you'll know a switch-hitter is someone who can bat both right-handed and left-handed.

In a similar way, Crossover Design allows subjects to experience multiple conditions, flipping them around so that everyone gets a turn in each role.

This design is like the utility player on our team—versatile, flexible, and really good at adapting.

The Crossover Design has its roots in medical research and has been popular since the mid-20th century. It's often used in clinical trials to test the effectiveness of different treatments.

Crossover Design Pros

The neat thing about this design is that it allows each participant to serve as their own control group. Imagine you're testing two new kinds of headache medicine. Instead of giving one type to one group and another type to a different group, you'd give both kinds to the same people but at different times.

Crossover Design Cons

What's the big deal with Crossover Design? Its major strength is in reducing the "noise" that comes from individual differences. Since each person experiences all conditions, it's easier to see real effects. However, there's a catch. This design assumes that there's no lasting effect from the first condition when you switch to the second one. That might not always be true. If the first treatment has a long-lasting effect, it could mess up the results when you switch to the second treatment.

Crossover Design Uses

A well-known example of Crossover Design is in studies that look at the effects of different types of diets—like low-carb vs. low-fat diets. Researchers might have participants follow a low-carb diet for a few weeks, then switch them to a low-fat diet. By doing this, they can more accurately measure how each diet affects the same group of people.

In our team of experimental designs, if True Experimental Design is the quarterback and Longitudinal Design is the wise elder, Factorial Design is the strategist, Cross-Sectional Design is the speedster, Correlational Design is the scout, Meta-Analysis is the coach, Non-Experimental Design is the journalist, and Repeated Measures Design is the time traveler, then Crossover Design is the versatile utility player—always ready to adapt and play multiple roles to get the most accurate results.

12) Cluster Randomized Design

Meet the Cluster Randomized Design, the team captain of group-focused research. In our imaginary lineup of experimental designs, if other designs focus on individual players, then Cluster Randomized Design is looking at how the entire team functions.

This approach is especially common in educational and community-based research, and it's been gaining traction since the late 20th century.

Here's how Cluster Randomized Design works: Instead of assigning individual people to different conditions, researchers assign entire groups, or "clusters." These could be schools, neighborhoods, or even entire towns. This helps you see how the new method works in a real-world setting.

Imagine you want to see if a new anti-bullying program really works. Instead of selecting individual students, you'd introduce the program to a whole school or maybe even several schools, and then compare the results to schools without the program.

Cluster Randomized Design Pros

Why use Cluster Randomized Design? Well, sometimes it's just not practical to assign conditions at the individual level. For example, you can't really have half a school following a new reading program while the other half sticks with the old one; that would be way too confusing! Cluster Randomization helps get around this problem by treating each "cluster" as its own mini-experiment.

Cluster Randomized Design Cons

There's a downside, too. Because entire groups are assigned to each condition, there's a risk that the groups might be different in some important way that the researchers didn't account for. That's like having one sports team that's full of veterans playing against a team of rookies; the match wouldn't be fair.

Cluster Randomized Design Uses

A famous example is the research conducted to test the effectiveness of different public health interventions, like vaccination programs. Researchers might roll out a vaccination program in one community but not in another, then compare the rates of disease in both.

In our metaphorical research team, if True Experimental Design is the quarterback, Longitudinal Design is the wise elder, Factorial Design is the strategist, Cross-Sectional Design is the speedster, Correlational Design is the scout, Meta-Analysis is the coach, Non-Experimental Design is the journalist, Repeated Measures Design is the time traveler, and Crossover Design is the utility player, then Cluster Randomized Design is the team captain—always looking out for the group as a whole.

13) Mixed-Methods Design

Say hello to Mixed-Methods Design, the all-rounder or the "Renaissance player" of our research team.

Mixed-Methods Design uses a blend of both qualitative and quantitative methods to get a more complete picture, just like a Renaissance person who's good at lots of different things. It's like being good at both offense and defense in a sport; you've got all your bases covered!

Mixed-Methods Design is a fairly new kid on the block, becoming more popular in the late 20th and early 21st centuries as researchers began to see the value in using multiple approaches to tackle complex questions. It's the Swiss Army knife in our research toolkit, combining the best parts of other designs to be more versatile.

Here's how it could work: Imagine you're studying the effects of a new educational app on students' math skills. You might use quantitative methods like tests and grades to measure how much the students improve—that's the 'numbers part.'

But you also want to know how the students feel about math now, or why they think they got better or worse. For that, you could conduct interviews or have students fill out journals—that's the 'story part.'

Mixed-Methods Design Pros

So, what's the scoop on Mixed-Methods Design? The strength is its versatility and depth; you're not just getting numbers or stories, you're getting both, which gives a fuller picture.

Mixed-Methods Design Cons

But, it's also more challenging. Imagine trying to play two sports at the same time! You have to be skilled in different research methods and know how to combine them effectively.

Mixed-Methods Design Uses

A high-profile example of Mixed-Methods Design is research on climate change. Scientists use numbers and data to show temperature changes (quantitative), but they also interview people to understand how these changes are affecting communities (qualitative).

In our team of experimental designs, if True Experimental Design is the quarterback, Longitudinal Design is the wise elder, Factorial Design is the strategist, Cross-Sectional Design is the speedster, Correlational Design is the scout, Meta-Analysis is the coach, Non-Experimental Design is the journalist, Repeated Measures Design is the time traveler, Crossover Design is the utility player, and Cluster Randomized Design is the team captain, then Mixed-Methods Design is the Renaissance player—skilled in multiple areas and able to bring them all together for a winning strategy.

14) Multivariate Design

Now, let's turn our attention to Multivariate Design, the multitasker of the research world.

If our lineup of research designs were like players on a basketball court, Multivariate Design would be the player dribbling, passing, and shooting all at once. This design doesn't just look at one or two things; it looks at several variables simultaneously to see how they interact and affect each other.

Multivariate Design is like baking a cake with many ingredients. Instead of just looking at how flour affects the cake, you also consider sugar, eggs, and milk all at once. This way, you understand how everything works together to make the cake taste good or bad.

Multivariate Design has been a go-to method in psychology, economics, and social sciences since the latter half of the 20th century. With the advent of computers and advanced statistical software, analyzing multiple variables at once became a lot easier, and Multivariate Design soared in popularity.

Multivariate Design Pros

So, what's the benefit of using Multivariate Design? Its power lies in its complexity. By studying multiple variables at the same time, you can get a really rich, detailed understanding of what's going on.

Multivariate Design Cons

But that complexity can also be a drawback. With so many variables, it can be tough to tell which ones are really making a difference and which ones are just along for the ride.

Multivariate Design Uses

Imagine you're a coach trying to figure out the best strategy to win games. You wouldn't just look at how many points your star player scores; you'd also consider assists, rebounds, turnovers, and maybe even how loud the crowd is. A Multivariate Design would help you understand how all these factors work together to determine whether you win or lose.

A well-known example of Multivariate Design is in market research. Companies often use this approach to figure out how different factors—like price, packaging, and advertising—affect sales. By studying multiple variables at once, they can find the best combination to boost profits.

In our metaphorical research team, if True Experimental Design is the quarterback, Longitudinal Design is the wise elder, Factorial Design is the strategist, Cross-Sectional Design is the speedster, Correlational Design is the scout, Meta-Analysis is the coach, Non-Experimental Design is the journalist, Repeated Measures Design is the time traveler, Crossover Design is the utility player, Cluster Randomized Design is the team captain, and Mixed-Methods Design is the Renaissance player, then Multivariate Design is the multitasker—juggling many variables at once to get a fuller picture of what's happening.

15) Pretest-Posttest Design

Let's introduce Pretest-Posttest Design, the "Before and After" superstar of our research team. You've probably seen those before-and-after pictures in ads for weight loss programs or home renovations, right?

Well, this design is like that, but for science! Pretest-Posttest Design checks out what things are like before the experiment starts and then compares that to what things are like after the experiment ends.

This design is one of the classics, a staple in research for decades across various fields like psychology, education, and healthcare. It's so simple and straightforward that it has stayed popular for a long time.

In Pretest-Posttest Design, you measure your subject's behavior or condition before you introduce any changes—that's your "before" or "pretest." Then you do your experiment, and after it's done, you measure the same thing again—that's your "after" or "posttest."

Pretest-Posttest Design Pros

What makes Pretest-Posttest Design special? It's pretty easy to understand and doesn't require fancy statistics.

Pretest-Posttest Design Cons

But there are some pitfalls. For example, what if the kids in our math example get better at multiplication just because they're older or because they've taken the test before? That would make it hard to tell if the program is really effective or not.

Pretest-Posttest Design Uses

Let's say you're a teacher and you want to know if a new math program helps kids get better at multiplication. First, you'd give all the kids a multiplication test—that's your pretest. Then you'd teach them using the new math program. At the end, you'd give them the same test again—that's your posttest. If the kids do better on the second test, you might conclude that the program works.

One famous use of Pretest-Posttest Design is in evaluating the effectiveness of driver's education courses. Researchers will measure people's driving skills before and after the course to see if they've improved.

16) Solomon Four-Group Design

Next up is the Solomon Four-Group Design, the "chess master" of our research team. This design is all about strategy and careful planning. Named after Richard L. Solomon who introduced it in the 1940s, this method tries to correct some of the weaknesses in simpler designs, like the Pretest-Posttest Design.

Here's how it rolls: The Solomon Four-Group Design uses four different groups to test a hypothesis. Two groups get a pretest, then one of them receives the treatment or intervention, and both get a posttest. The other two groups skip the pretest, and only one of them receives the treatment before they both get a posttest.

Sound complicated? It's like playing 4D chess; you're thinking several moves ahead!

Solomon Four-Group Design Pros

What's the pro and con of the Solomon Four-Group Design? On the plus side, it provides really robust results because it accounts for so many variables.

Solomon Four-Group Design Cons

The downside? It's a lot of work and requires a lot of participants, making it more time-consuming and costly.

Solomon Four-Group Design Uses

Let's say you want to figure out if a new way of teaching history helps students remember facts better. Two classes take a history quiz (pretest), then one class uses the new teaching method while the other sticks with the old way. Both classes take another quiz afterward (posttest).

Meanwhile, two more classes skip the initial quiz, and then one uses the new method before both take the final quiz. Comparing all four groups will give you a much clearer picture of whether the new teaching method works and whether the pretest itself affects the outcome.

The Solomon Four-Group Design is less commonly used than simpler designs but is highly respected for its ability to control for more variables. It's a favorite in educational and psychological research where you really want to dig deep and figure out what's actually causing changes.

17) Adaptive Designs

Now, let's talk about Adaptive Designs, the chameleons of the experimental world.

Imagine you're a detective, and halfway through solving a case, you find a clue that changes everything. You wouldn't just stick to your old plan; you'd adapt and change your approach, right? That's exactly what Adaptive Designs allow researchers to do.

In an Adaptive Design, researchers can make changes to the study as it's happening, based on early results. In a traditional study, once you set your plan, you stick to it from start to finish.

Adaptive Design Pros

This method is particularly useful in fast-paced or high-stakes situations, like developing a new vaccine in the middle of a pandemic. The ability to adapt can save both time and resources, and more importantly, it can save lives by getting effective treatments out faster.

Adaptive Design Cons

But Adaptive Designs aren't without their drawbacks. They can be very complex to plan and carry out, and there's always a risk that the changes made during the study could introduce bias or errors.

Adaptive Design Uses

Adaptive Designs are most often seen in clinical trials, particularly in the medical and pharmaceutical fields.

For instance, if a new drug is showing really promising results, the study might be adjusted to give more participants the new treatment instead of a placebo. Or if one dose level is showing bad side effects, it might be dropped from the study.

The best part is, these changes are pre-planned. Researchers lay out in advance what changes might be made and under what conditions, which helps keep everything scientific and above board.

In terms of applications, besides their heavy usage in medical and pharmaceutical research, Adaptive Designs are also becoming increasingly popular in software testing and market research. In these fields, being able to quickly adjust to early results can give companies a significant advantage.

Adaptive Designs are like the agile startups of the research world—quick to pivot, keen to learn from ongoing results, and focused on rapid, efficient progress. However, they require a great deal of expertise and careful planning to ensure that the adaptability doesn't compromise the integrity of the research.

18) Bayesian Designs

Next, let's dive into Bayesian Designs, the data detectives of the research universe. Named after Thomas Bayes, an 18th-century statistician and minister, this design doesn't just look at what's happening now; it also takes into account what's happened before.

Imagine if you were a detective who not only looked at the evidence in front of you but also used your past cases to make better guesses about your current one. That's the essence of Bayesian Designs.

Bayesian Designs are like detective work in science. As you gather more clues (or data), you update your best guess on what's really happening. This way, your experiment gets smarter as it goes along.

In the world of research, Bayesian Designs are most notably used in areas where you have some prior knowledge that can inform your current study. For example, if earlier research shows that a certain type of medicine usually works well for a specific illness, a Bayesian Design would include that information when studying a new group of patients with the same illness.

Bayesian Design Pros

One of the major advantages of Bayesian Designs is their efficiency. Because they use existing data to inform the current experiment, often fewer resources are needed to reach a reliable conclusion.

Bayesian Design Cons

However, they can be quite complicated to set up and require a deep understanding of both statistics and the subject matter at hand.

Bayesian Design Uses

Bayesian Designs are highly valued in medical research, finance, environmental science, and even in Internet search algorithms. Their ability to continually update and refine hypotheses based on new evidence makes them particularly useful in fields where data is constantly evolving and where quick, informed decisions are crucial.

Here's a real-world example: In the development of personalized medicine, where treatments are tailored to individual patients, Bayesian Designs are invaluable. If a treatment has been effective for patients with similar genetics or symptoms in the past, a Bayesian approach can use that data to predict how well it might work for a new patient.

This type of design is also increasingly popular in machine learning and artificial intelligence. In these fields, Bayesian Designs help algorithms "learn" from past data to make better predictions or decisions in new situations. It's like teaching a computer to be a detective that gets better and better at solving puzzles the more puzzles it sees.

19) Covariate Adaptive Randomization

Now let's turn our attention to Covariate Adaptive Randomization, which you can think of as the "matchmaker" of experimental designs.

Picture a soccer coach trying to create the most balanced teams for a friendly match. They wouldn't just randomly assign players; they'd take into account each player's skills, experience, and other traits.

Covariate Adaptive Randomization is all about creating the most evenly matched groups possible for an experiment.

In traditional randomization, participants are allocated to different groups purely by chance. This is a pretty fair way to do things, but it can sometimes lead to unbalanced groups.

Imagine if all the professional-level players ended up on one soccer team and all the beginners on another; that wouldn't be a very informative match! Covariate Adaptive Randomization fixes this by using important traits or characteristics (called "covariates") to guide the randomization process.

Covariate Adaptive Randomization Pros

The benefits of this design are pretty clear: it aims for balance and fairness, making the final results more trustworthy.

Covariate Adaptive Randomization Cons

But it's not perfect. It can be complex to implement and requires a deep understanding of which characteristics are most important to balance.

Covariate Adaptive Randomization Uses

This design is particularly useful in medical trials. Let's say researchers are testing a new medication for high blood pressure. Participants might have different ages, weights, or pre-existing conditions that could affect the results.

Covariate Adaptive Randomization would make sure that each treatment group has a similar mix of these characteristics, making the results more reliable and easier to interpret.

In practical terms, this design is often seen in clinical trials for new drugs or therapies, but its principles are also applicable in fields like psychology, education, and social sciences.

For instance, in educational research, it might be used to ensure that classrooms being compared have similar distributions of students in terms of academic ability, socioeconomic status, and other factors.

Covariate Adaptive Randomization is like the wise elder of the group, ensuring that everyone has an equal opportunity to show their true capabilities, thereby making the collective results as reliable as possible.

20) Stepped Wedge Design

Let's now focus on the Stepped Wedge Design, a thoughtful and cautious member of the experimental design family.

Imagine you're trying out a new gardening technique, but you're not sure how well it will work. You decide to apply it to one section of your garden first, watch how it performs, and then gradually extend the technique to other sections. This way, you get to see its effects over time and across different conditions. That's basically how Stepped Wedge Design works.

In a Stepped Wedge Design, all participants or clusters start off in the control group, and then, at different times, they 'step' over to the intervention or treatment group. This creates a wedge-like pattern over time where more and more participants receive the treatment as the study progresses. It's like rolling out a new policy in phases, monitoring its impact at each stage before extending it to more people.

Stepped Wedge Design Pros

The Stepped Wedge Design offers several advantages. Firstly, it allows for the study of interventions that are expected to do more good than harm, which makes it ethically appealing.

Secondly, it's useful when resources are limited and it's not feasible to roll out a new treatment to everyone at once. Lastly, because everyone eventually receives the treatment, it can be easier to get buy-in from participants or organizations involved in the study.

Stepped Wedge Design Cons

However, this design can be complex to analyze because it has to account for both the time factor and the changing conditions in each 'step' of the wedge. And like any study where participants know they're receiving an intervention, there's the potential for the results to be influenced by the placebo effect or other biases.

Stepped Wedge Design Uses

This design is particularly useful in health and social care research. For instance, if a hospital wants to implement a new hygiene protocol, it might start in one department, assess its impact, and then roll it out to other departments over time. This allows the hospital to adjust and refine the new protocol based on real-world data before it's fully implemented.

In terms of applications, Stepped Wedge Designs are commonly used in public health initiatives, organizational changes in healthcare settings, and social policy trials. They are particularly useful in situations where an intervention is being rolled out gradually and it's important to understand its impacts at each stage.

21) Sequential Design

Next up is Sequential Design, the dynamic and flexible member of our experimental design family.

Imagine you're playing a video game where you can choose different paths. If you take one path and find a treasure chest, you might decide to continue in that direction. If you hit a dead end, you might backtrack and try a different route. Sequential Design operates in a similar fashion, allowing researchers to make decisions at different stages based on what they've learned so far.

In a Sequential Design, the experiment is broken down into smaller parts, or "sequences." After each sequence, researchers pause to look at the data they've collected. Based on those findings, they then decide whether to stop the experiment because they've got enough information, or to continue and perhaps even modify the next sequence.

Sequential Design Pros

This allows for a more efficient use of resources, as you're only continuing with the experiment if the data suggests it's worth doing so.

One of the great things about Sequential Design is its efficiency. Because you're making data-driven decisions along the way, you can often reach conclusions more quickly and with fewer resources.

Sequential Design Cons

However, it requires careful planning and expertise to ensure that these "stop or go" decisions are made correctly and without bias.

Sequential Design Uses

In terms of its applications, besides healthcare and medicine, Sequential Design is also popular in quality control in manufacturing, environmental monitoring, and financial modeling. In these areas, being able to make quick decisions based on incoming data can be a big advantage.

This design is often used in clinical trials involving new medications or treatments. For example, if early results show that a new drug has significant side effects, the trial can be stopped before more people are exposed to it.

On the flip side, if the drug is showing promising results, the trial might be expanded to include more participants or to extend the testing period.

Think of Sequential Design as the nimble athlete of experimental designs, capable of quick pivots and adjustments to reach the finish line in the most effective way possible. But just like an athlete needs a good coach, this design requires expert oversight to make sure it stays on the right track.

22) Field Experiments

Last but certainly not least, let's explore Field Experiments—the adventurers of the experimental design world.

Picture a scientist leaving the controlled environment of a lab to test a theory in the real world, like a biologist studying animals in their natural habitat or a social scientist observing people in a real community. These are Field Experiments, and they're all about getting out there and gathering data in real-world settings.

Field Experiments embrace the messiness of the real world, unlike laboratory experiments, where everything is controlled down to the smallest detail. This makes them both exciting and challenging.

Field Experiment Pros

On one hand, the results often give us a better understanding of how things work outside the lab.

While Field Experiments offer real-world relevance, they come with challenges like controlling for outside factors and the ethical considerations of intervening in people's lives without their knowledge.

Field Experiment Cons

On the other hand, the lack of control can make it harder to tell exactly what's causing what. Yet, despite these challenges, they remain a valuable tool for researchers who want to understand how theories play out in the real world.

Field Experiment Uses

Let's say a school wants to improve student performance. In a Field Experiment, they might change the school's daily schedule for one semester and keep track of how students perform compared to another school where the schedule remained the same.

Because the study is happening in a real school with real students, the results could be very useful for understanding how the change might work in other schools. But since it's the real world, lots of other factors—like changes in teachers or even the weather—could affect the results.

Field Experiments are widely used in economics, psychology, education, and public policy. For example, you might have heard of the famous "Broken Windows" experiment in the 1980s that looked at how small signs of disorder, like broken windows or graffiti, could encourage more serious crime in neighborhoods. This experiment had a big impact on how cities think about crime prevention.

From the foundational concepts of control groups and independent variables to the sophisticated layouts like Covariate Adaptive Randomization and Sequential Design, it's clear that the realm of experimental design is as varied as it is fascinating.

We've seen that each design has its own special talents, ideal for specific situations. Some designs, like the Classic Controlled Experiment, are like reliable old friends you can always count on.

Others, like Sequential Design, are flexible and adaptable, making quick changes based on what they learn. And let's not forget the adventurous Field Experiments, which take us out of the lab and into the real world to discover things we might not see otherwise.

Choosing the right experimental design is like picking the right tool for the job. The method you choose can make a big difference in how reliable your results are and how much people will trust what you've discovered. And as we've learned, there's a design to suit just about every question, every problem, and every curiosity.

So the next time you read about a new discovery in medicine, psychology, or any other field, you'll have a better understanding of the thought and planning that went into figuring things out. Experimental design is more than just a set of rules; it's a structured way to explore the unknown and answer questions that can change the world.

Related posts:

• Experimental Psychologist Career (Salary + Duties + Interviews)
• 40+ Famous Psychologists (Images + Biographies)
• 11+ Psychology Experiment Ideas (Goals + Methods)
• The Little Albert Experiment
• 41+ White Collar Job Examples (Salary + Path)

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Design of Experiments

DOE, or Design of Experiments, is a branch of applied statistics that uses planning, conducting, analyzing, and interpreting controlled tests to explain the variation of information under conditions hypothesized to reflect the variation. It’s a powerful data collection and analysis tool that investigates how different factors or variables affect an outcome or response of interest.

Design of Experiments (DOE) is also referred to as Designed Experiments or Experimental Design - all of the terms have the same meaning.

The term experiment is defined as the systematic procedure carried out under controlled conditions in order to discover an unknown effect, to test or establish a hypothesis, or to illustrate a known effect. When analyzing a process, experiments are often used to evaluate which process inputs have a significant impact on the process output and what the target level of those inputs should be to achieve a desired result (output). Experiments can be designed in many different ways to collect this information, and it's helpful to have software that guides you in the most accurate direction to answer your research questions. EngineRoom's DOE tool has built-in features that specifically cater to helping you design statistically sound experiments. It guides you through selecting a design streamlined in favor of the resources needed, but it's also powerful enough to detect an effect if it exists.

Experimental design can be used at the point of greatest leverage to reduce design costs by speeding up the design process, reducing late engineering design changes, and reducing product material and labor complexity. Designed Experiments are also powerful tools to achieve manufacturing cost savings by minimizing process variation and reducing rework, scrap, and the need for inspection.

This Toolbox module includes a general overview of Experimental Design and links and other resources to assist you in conducting designed experiments. A glossary of terms is also available at any time through the Help function, and we recommend that you read through it to familiarize yourself with any unfamiliar terms. For an additional resource, check out the web recording of our two-part webinar, Getting Started with DOE.

Preparation

If you do not have a general knowledge of statistics, review the Histogram , Statistical Process Control , and Regression and Correlation Analysis modules of the Toolbox prior to working with this module.

You can use the MoreSteam's data analysis software EngineRoom® to create and analyze many commonly used but powerful experimental designs.

Components of Experimental Design

Consider the following diagram of a cake-baking process (Figure 1). There are three aspects of the process that are analyzed by a designed experiment:

• Factors , or inputs to the process. Factors can be classified as either controllable or uncontrollable variables. In this case, the controllable factors are the ingredients for the cake and the oven that the cake is baked in. The controllable variables will be referred to throughout the material as factors. Note that the ingredients list was shortened for this example - there could be many other ingredients that have a significant bearing on the end result (oil, water, flavoring, etc). Likewise, there could be other types of factors, such as the mixing method or tools, the sequence of mixing, or even the people involved. People are generally considered a Noise Factor (see the glossary) - an uncontrollable factor that causes variability under normal operating conditions, but we can control it during the experiment using blocking and randomization. Potential factors can be categorized using the Fishbone Chart (Cause & Effect Diagram) available from the Toolbox.
• Levels , or settings of each factor in the study. Examples include the oven temperature setting and the particular amounts of sugar, flour, and eggs chosen for evaluation.
• Response , or output of the experiment. In the case of cake baking, the taste, consistency, and appearance of the cake are measurable outcomes potentially influenced by the factors and their respective levels. Experimenters often desire to avoid optimizing the process for one response at the expense of another. For this reason, important outcomes are measured and analyzed to determine the factors and their settings that will provide the best overall outcome for the critical-to-quality characteristics - both measurable variables and assessable attributes.

Purpose of Experimentation

Designed experiments have many potential uses in improving processes and products, including:

• Comparing Alternatives. In the case of our cake-baking example, we might want to compare the results from two different types of flour. If it turned out that the flour from different vendors was not significant, we could select the lowest-cost vendor. If flour were significant, then we would select the best flour. The experiment(s) should allow us to make an informed decision that evaluates both quality and cost.
• Identifying the Significant Inputs (Factors) Affecting an Output (Response) - separating the vital few from the trivial many . We might ask a question: "What are the significant factors beyond flour, eggs, sugar and baking?"
• Achieving an Optimal Process Output (Response). "What are the necessary factors, and what are the levels of those factors, to achieve the exact taste and consistency of Mom's chocolate cake?
• Reducing Variability . "Can the recipe be changed so it is more likely to always come out the same?"
• Minimizing, Maximizing, or Targeting an Output (Response). "How can the cake be made as moist as possible without disintegrating?"
• Improving process or product " Robustness " - fitness for use under varying conditions. "Can the factors and their levels (recipe) be modified so the cake will come out nearly the same no matter what type of oven is used?"
• Balancing Tradeoffs when there are multiple Critical to Quality Characteristics (CTQC's) that require optimization. "How do you produce the best tasting cake with the simplest recipe (least number of ingredients) and shortest baking time?"

Experiment Design Guidelines

The Design of an experiment addresses the questions outlined above by stipulating the following:

• The factors to be tested.
• The levels of those factors.
• The structure and layout of experimental runs, or conditions.

A well-designed experiment is as simple as possible - obtaining the required information in a cost effective and reproducible manner.

MoreSteam.com Reminder: Like Statistical Process Control, reliable experiment results are predicated upon two conditions: a capable measurement system, and a stable process. If the measurement system contributes excessive error, the experiment results will be muddied. You can use the Measurement Systems Analysis module from the Toolbox to evaluate the measurement system before you conduct your experiment.

Likewise, you can use the Statistical Process Control module to help you evaluate the statistical stability of the process being evaluated. Variation impacting the response must be limited to common cause random error - not special cause variation from specific events.

When designing an experiment, pay particular heed to four potential traps that can create experimental difficulties:

1. In addition to measurement error (explained above), other sources of error, or unexplained variation , can obscure the results. Note that the term "error" is not a synonym with "mistakes". Error refers to all unexplained variation that is either within an experiment run or between experiment runs and associated with level settings changing. Properly designed experiments can identify and quantify the sources of error.

2. Uncontrollable factors that induce variation under normal operating conditions are referred to as " Noise Factors ". These factors, such as multiple machines, multiple shifts, raw materials, humidity, etc., can be built into the experiment so that their variation doesn't get lumped into the unexplained, or experiment error. A key strength of Designed Experiments is the ability to determine factors and settings that minimize the effects of the uncontrollable factors.

3. Correlation can often be confused with causation. Two factors that vary together may be highly correlated without one causing the other - they may both be caused by a third factor. Consider the example of a porcelain enameling operation that makes bathtubs. The manager notices that there are intermittent problems with "orange peel" - an unacceptable roughness in the enamel surface. The manager also notices that the orange peel is worse on days with a low production rate. A plot of orange peel vs. production volume below (Figure 2) illustrates the correlation:

If the data are analyzed without knowledge of the operation, a false conclusion could be reached that low production rates cause orange peel. In fact, both low production rates and orange peel are caused by excessive absenteeism - when regular spray booth operators are replaced by employees with less skill. This example highlights the importance of factoring in operational knowledge when designing an experiment. Brainstorming exercises and Fishbone Cause & Effect Diagrams are both excellent techniques available through the Toolbox to capture this operational knowledge during the design phase of the experiment. The key is to involve the people who live with the process on a daily basis.

4. The combined effects or interactions between factors demand careful thought prior to conducting the experiment. For example, consider an experiment to grow plants with two inputs: water and fertilizer. Increased amounts of water are found to increase growth, but there is a point where additional water leads to root-rot and has a detrimental impact. Likewise, additional fertilizer has a beneficial impact up to the point that too much fertilizer burns the roots. Compounding this complexity of the main effects, there are also interactive effects - too much water can negate the benefits of fertilizer by washing it away. Factors may generate non-linear effects that are not additive, but these can only be studied with more complex experiments that involve more than 2 level settings. Two levels is defined as linear (two points define a line), three levels are defined as quadratic (three points define a curve), four levels are defined as cubic, and so on.

Experiment Design Process

The flow chart below (Figure 3) illustrates the experiment design process:

Test of Means - One Factor Experiment

One of the most common types of experiments is the comparison of two process methods, or two methods of treatment. There are several ways to analyze such an experiment depending upon the information available from the population as well as the sample. One of the most straight-forward methods to evaluate a new process method is to plot the results on an SPC chart that also includes historical data from the baseline process, with established control limits.

Then apply the standard rules to evaluate out-of-control conditions to see if the process has been shifted. You may need to collect several sub-groups worth of data in order to make a determination, although a single sub-group could fall outside of the existing control limits. You can link to the Statistical Process Control charts module of the Toolbox for help.

An alternative to the control chart approach is to use the F-test (F-ratio) to compare the means of alternate treatments. This is done automatically by the ANOVA (Analysis of Variance) function of statistical software, but we will illustrate the calculation using the following example: A commuter wanted to find a quicker route home from work. There were two alternatives to bypass traffic bottlenecks. The commuter timed the trip home over a month and a half, recording ten data points for each alternative.

MoreSteam Reminder: Take care to make sure your experimental runs are randomized - i.e., run in random order. Randomization is necessary to avoid the impact of lurking variables. Consider the example of measuring the time to drive home: if a major highway project is started at the end of the sample period increases commute time, then the highway project could bias the results if a given treatment (route) is sampled during that time period.

Scheduling the experimental runs is necessary to ensure independence of observations. You can randomize your runs using pennies - write the reference number for each run on a penny with a pencil, then draw the pennies from a container and record the order.

The data are shown below along with the mean for each route (treatment), and the variance for each route:

As shown on the table above, both new routes home (B&C) appear to be quicker than the existing route A. To determine whether the difference in treatment means is due to random chance or a statistically significant different process, an ANOVA F-test is performed.

The F-test analysis is the basis for model evaluation of both single factor and multi-factor experiments. This analysis is commonly output as an ANOVA table by statistical analysis software, as illustrated by the table below:

The most important output of the table is the F-ratio (3.61). The F-ratio is equivalent to the Mean Square (variation) between the groups (treatments, or routes home in our example) of 19.9 divided by the Mean Square error within the groups (variation within the given route samples) of 5.51.

The Model F-ratio of 3.61 implies the model is significant.The p-value ('Probability of exceeding the observed F-ratio assuming no significant differences among the means') of 0.0408 indicates that there is only a 4.08% probability that a Model F-ratio this large could occur due to noise (random chance). In other words, the three routes differ significantly in terms of the time taken to reach home from work.

The following graph (Figure 4) shows 'Simultaneous Pairwise Difference' Confidence Intervals for each pair of differences among the treatment means. If an interval includes the value of zero (meaning 'zero difference'), the corresponding pair of means do NOT differ significantly. You can use these intervals to identify which of the three routes is different and by how much. The intervals contain the likely values of differences of treatment means (1-2), (1-3) and (2-3) respectively, each of which is likely to contain the true (population) mean difference in 95 out of 100 samples. Notice the second interval (1-3) does not include the value of zero; the means of routes 1 (A) and 3 (C) differ significantly. In fact, all values included in the (1, 3) interval are positive, so we can say that route 1 (A) has a longer commute time associated with it compared to route 3 (C).

Other statistical approaches to the comparison of two or more treatments are available through the online statistics handbook - Chapter 7: Statistics Handbook .

Multi-Factor Designed Experiments

Multi-factor experiments are designed to evaluate multiple factors set at multiple levels. One approach is called a Full Factorial experiment, in which each factor is tested at each level in every possible combination with the other factors and their levels. Full factorial experiments that study all paired interactions can be economic and practical if there are few factors and only 2 or 3 levels per factor. The advantage is that all paired interactions can be studied. However, the number of runs goes up exponentially as additional factors are added. Experiments with many factors can quickly become unwieldy and costly to execute, as shown by the chart below:

See a Full Factorial Experiment in EngineRoom:

To study higher numbers of factors and interactions, Fractional Factorial designs can be used to reduce the number of runs by evaluating only a subset of all possible combinations of the factors. These designs are very cost effective, but the study of interactions between factors is limited, so the experimental layout must be decided before the experiment can be run (during the experiment design phase).

MoreSteam Reminder: When selecting the factor levels for an experiment, it is critical to capture the natural variation of the process. Levels that are close to the process mean may hide the significance of factor over its likely range of values. For factors that are measured on a variable scale, try to select levels at plus/minus three standard deviations from the mean value.

You can also use EngineRoom , MoreSteam's online statistical tool, to design and analyze several popular designed experiments. The application includes tutorials on planning and executing full, fractional and general factorial designs.

See a Fractional Factorial Experiment in EngineRoom:

Advanced Topic - Taguchi Methods

Dr. Genichi Taguchi is a Japanese statistician and Deming prize winner who pioneered techniques to improve quality through Robust Design of products and production processes. Dr. Taguchi developed fractional factorial experimental designs that use a very limited number of experimental runs. The specifics of Taguchi experimental design are beyond the scope of this tutorial, however, it is useful to understand Taguchi's Loss Function, which is the foundation of his quality improvement philosophy.

Traditional thinking is that any part or product within specification is equally fit for use. In that case, loss (cost) from poor quality occurs only outside the specification (Figure 5). However, Taguchi makes the point that a part marginally within the specification is really little better than a part marginally outside the specification.

As such, Taguchi describes a continuous Loss Function that increases as a part deviates from the target, or nominal value (Figure 6). The Loss Function stipulates that society's loss due to poorly performing products is proportional to the square of the deviation of the performance characteristic from its target value.

Taguchi adds this cost to society (consumers) of poor quality to the production cost of the product to arrive at the total loss (cost). Taguchi uses designed experiments to produce product and process designs that are more robust - less sensitive to part/process variation.

Choosing the Right DOE Software

When planning a DOE, it is essential to use statistical software that helps you design and analyze the most appropriate experiment to answer your research questions. EngineRoom's DOE tool has built-in features specifically designed to guide you through selecting a design streamlined in favor of the resources needed but also powerful enough to detect an effect if it exists.

It provides a comprehensive list of full, fractional, and general factorial designs to cover a wide variety of DOE scenarios. It also allows you to run automated algorithms to select the best model for the data, making it easier to draw conclusions and take informed actions. Using EngineRoom for your designed experiments can save time, reduce costly errors, and help make data-driven decisions.

See a General Factorial Experiment in EngineRoom:

Designed experiments are an advanced and powerful analysis tool during projects. An effective experimenter can filter out noise and discover significant process factors. The factors can then be used to control response properties in a process and teams can then engineer a process to the exact specification their product or service requires.

A well built experiment can save not only project time but also solve critical problems which have remained unseen in processes. Specifically, interactions of factors can be observed and evaluated. Ultimately, teams will learn what factors matter and what factors do not.

Learn more about EngineRoom

• Webster's Ninth New Collegiate Dictionary

Additional Online Resources

• An excellent online Statistics Handbook is available that covers Design of Experiments and many other topics. See Section 5 - "Improve" for a complete tutorial on Design of Experiments.
• Check the White Paper Section for related online articles.
• Mark J. Anderson and Patrick J. Whitcomb, DOE Simplifie d (Productivity, Inc. 2000). ISBN 1-56327-225-3. Recommended - This book is easy to understand and comes with copy of excellent D.O.E. software good for 180 days.
• George E. P. Box, William G. Hunter and J. Stuart Hunter, Statistics for Experimenters - An Introduction to Design, Data Analysis, and Model Building (John Wiley and Sons, Inc. 1978). ISBN 0-471-09315-7
• Douglas C. Montgomery, Design and Analysis of Experiments (John Wiley & Sons, Inc., 1984) ISBN 0-471-86812-4.
• Genichi Taguchi, Introduction to Quality Engineering - Designing Quality Into Products and Processes (Asian Productivity Organization, 1986). ISBN 92-833-1084-5

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Experimental Designs

Statistics deals with the study of gathering, observing, calculating, and interpreting numerical data. It is full of experiments and research. A statistical experiment is defined as an ordered procedure which is performed with the objective of verifying, and determining the validity of the hypothesis. Before performing any experiment, some specific questions for which the experiment is intended should be clearly identified. To minimise the variability effect on the result of interest, the experiment has to be designed. So, the researcher will design the experiments for the purpose of improvement of precision. It is called experimental design or the design of experiments(DOE). In this article, let us discuss the definition and example of experimental design in detail.

Experimental Design Definition

In Statistics, the experimental design or the design of experiment (DOE) is defined as the design of an information-gathering experiment in which a variation is present or not, and it should be performed under the full control of the researcher. This term is generally used for controlled experiments. These experiments minimise the effects of the variable to increase the reliability of the results. In this design, the process of an experimental unit may include a group of people, plants, animals, etc.

Types of Experimental Designs

There are different types of experimental designs of research. They are:

Pre-experimental Research Design

True-experimental research design.

• Quasi-Experimental Research Design

In this article, we are going to discuss these different experimental designs for research with examples.

The simplest form of experimental research design in Statistics is the pre-experimental research design. In this method, a group or various groups are kept under observation, after some factors are recognised for the cause and effect. This method is usually conducted in order to understand whether further investigations are needed for the targeted group. That is why this process is considered to be cost-effective. This method is classified into three types, namely,

• Static Group Comparison
• One-group Pretest-posttest Experimental Research Design
• One-shot Case Study Experimental Research Design

This is the most accurate form of experimental research design as it relies on the statistical hypothesis to prove or disprove the hypothesis. This is the most commonly used method implemented in Physical Science. True experimental research design is the only method that establishes the cause and effect relationship within the groups. The factors which need to be satisfied in this method are:

• Random variable
• Variable can be manipulated by the researcher
• Control Groups (A group of participants are familiar with the experimental group, but the experimental rules do not apply to them)
• Experimental Group (Research participants where experimental rules are applied)

Quasi-Experimental Design

A quasi-experimental design is similar to a true experimental design, but there is a difference between the two.

In a true experiment design, the participants of the group are randomly assigned. So, every unit has an equal chance of getting into the experimental group.

In a quasi-experimental design, the participants of the groups are not randomly assigned. So, the researcher cannot make a cause or effect conclusion. Thus, it is not possible to assign the participants to the group.

Apart from these types of experimental design research in statistics, there are other two methods used in the research process such as randomized block design and completely randomized design.

Randomised Block Design

The randomised block design is preferred in the case when the researcher is clear about the distinct difference among the group of objects. In this design, the experimental units are classified into subgroups of similar categories. Those groups are randomly assigned to the group of treatment. The blocks are classified in such a way in the variability within each block should be less than the variability among the blocks. This block design is quite efficient as it reduces the variability and produces a better estimation.

In a drug testing experiment, the researcher believes that age is the most significant factor. So he divides the units according to the age groups such as

• Under 15 years old
• 15 – 35 years old
• 36 – 55 years old
• Over 55 years old

Completely Randomised Design

Of all the types, the simplest type of experimental design is the completely randomized design, in which the participants are randomly assigned to the treatment groups. The main advantage of using this method is that it avoids bias and controls the role of chance. This method provides a solid foundation for Statistical analysis as it allows the use of probability theory.

Application of Experimental Design

The concept of experimental design is applied to Engineering, Natural Science and Social Science as well. The areas in which the experimental designs used are:

• Evaluation of physical structures, materials and components
• Chemical formulations
• Computer programs
• Opinion polls
• Natural experiments
• Statistical surveys

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We use case studies to explore how to use DOE methods to choose small subsets of trials and how to create models to make powerful predictions. These models can accurately predict the entire NMR or Raman spectra of any of the formulations not used in the experimental design and – given the spectra for a mixture with unknown proportions – the formula for a blend.

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• General & Introductory Industrial Engineering

Design of Experiments: A Modern Approach, 1st Edition

ISBN: 978-1-119-61119-6

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Bradley Jones , Douglas C. Montgomery

Design of Experiments: A Modern Approach introduces readers to planning and conducting experiments, analyzing the resulting data, and obtaining valid and objective conclusions. This innovative textbook uses design optimization as its design construction approach, focusing on practical experiments in engineering, science, and business rather than orthogonal designs and extensive analysis. Requiring only first-course knowledge of statistics and familiarity with matrix algebra, student-friendly chapters cover the design process for a range of various types of experiments.

The text follows a traditional outline for a design of experiments course, beginning with an introduction to the topic, historical notes, a review of fundamental statistics concepts, and a systematic process for designing and conducting experiments. Subsequent chapters cover simple comparative experiments, variance analysis, two-factor factorial experiments, randomized complete block design, response surface methodology, designs for nonlinear models, and more. Readers gain a solid understanding of the role of experimentation in technology commercialization and product realization activities—including new product design, manufacturing process development, and process improvement—as well as many applications of designed experiments in other areas such as marketing, service operations, e-commerce, and general business operations.

• Uses flexible, practically-applicable design optimization as design construction approach to address the unique features of a design problem
• Reviews basic statistical and experiment design concepts and methods
• Covers the four basic principles of experimental design: the factorial principle, randomization, replication, and blocking
• Presents definitive screening designs as a three-level alternative to standard screening designs
• Relies on software for calculation and analysis of important design material
• Includes numerous charts, graphs, tables, illustrations, and end-of-chapter problems

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• Published: 25 August 2024

Molecular dynamics and experimental analysis of energy behavior during stress relaxation in magnetorheological elastomers

• Nurul Hakimah Lazim 1 ,
• Mohd Aidy Faizal Johari 1 ,
• Saiful Amri Mazlan 1 , 2 ,
• Nur Azmah Nordin 1 ,
• Shahir Mohd Yusuf 1 &
• Michal Sedlacik 3 , 4  

Scientific Reports volume  14 , Article number:  19724 ( 2024 ) Cite this article

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• Energy science and technology
• Materials science

The diverse applications of magnetorheological elastomer (MRE) drive efforts to understand consistent performance and resistance to failure. Stress relaxation can lead to molecular chain deterioration, degradation in stiffness and rheological properties, and ultimately affect the life cycle of MRE. However, quantifying the energy and molecular dynamics during stress relaxation is challenging due to the difficulty of obtaining atomic-level insights experimentally. This study employs molecular dynamics (MD) simulation to elucidate the stress relaxation in MRE during constant strain. Magnetorheological elastomer models incorporating silicone rubber filled with varying magnetic iron particles (50–80 wt%) were constructed. Experimental results from an oscillatory shear rheometer showed the linear viscoelastic region of MRE to be within 0.001–0.01% strain. The simulation results indicated that stress relaxation has occurred, with stored energies decreased by 8.63–52.7% in all MRE models. Monitoring changes in energy components, the highest final stored energy (12,045 kJ) of the MRE model with 80 wt% Fe particles was primarily attributed to stronger intramolecular and intermolecular interactions, revealed by higher potential energy (3262 kJ) and van der Waals energy (− 2717.29 kJ). Stress relaxation also altered the molecular dynamics of this MRE model as evidenced by a decrease in kinetic energy (9362 kJ) and mean square displacement value (20,318 Å 2 ). The MD simulation provides a promising quantitative tool for elucidating stress relaxation, preventing material failure and offering insights for the design of MRE in the nanotechnology industry.

Introduction

Magnetorheological elastomer (MRE) has been widely used in various applications, including energy absorption, shock absorption, and vibration isolation systems for building and bridges, owing to tunable rheological properties when subjected to an external magnetic field. Generally, MRE exhibit the linear viscoelastic (LVE) region that represents an initial reversible deformation range where the molecular chains undergo insignificant rearrangement and can spontaneously return to their original form 1 . In addition, during LVE region, MRE could store elastic energy and resist deformation up to certain limit 2 . However, it is important to note that unlike purely elastic materials, MRE also exhibit viscous behavior. This means that over time, MRE can undergo time-dependent deformation and causes a gradual decline in properties of MRE. The time-dependent deformation in materials is often related to stress relaxation and fatigue phenomena. Fatigue refers to the progressive and localized structural damage that occurs when a material is subjected to cyclic loading or repeated stress over time 3 , while stress relaxation refers to the gradual decrease in stress in a material subjected to a constant strain over time 4 . The stress relaxation in MRE has raised concerns because it could lead to the deterioration in molecular chains and crosslink structures over a period of service. Additionally, stress relaxation can have significant implications for mechanical behavior of materials and may affect their structural integrity and performance in MRE. Consequently, this type of micro-deformation may limit the application of MRE to be used as flexible materials in energy and nanotechnology industries.

Johari et al. 5 has evaluated the durability performance of MRE using oscillatory shear rheometer for a total of 6010 s under constant strain of 0.01%. The study discovered that the storage modulus of MRE decreased by 0.5% by the end of test duration, indicating a stress relaxation phenomenon. Johari et al. 6 also utilized an oscillatory shear test for a duration of 84,000 s on MRE and reported the stress relaxation has developed strain localization and produced microplasticity in the shear band. Consequently, the shear stress, storage modulus and normal force of tested MRE decreased over this time of period. Study of stress relaxation phenomenon could provide insights about the durability performance for MRE to be used in long-term applications such as gaskets, seals, dampers and actuators 7 . Besides the experimental approach, another recent study by Nam and coworkers 8 presented both experimental and numerical simulations of isotropic and anisotropic MREs over 10 h using a single relaxation test. The work revealed that the shear stress and relaxation modulus under a strong magnetic field declined considerably after 0.25 h of testing. In a previous study, Nam et al. 9 also conducted single and multi-step relaxation tests using isotropic MREs for 1 h and found that the shear stress and relaxation modulus of MRE samples decreased over time, even at different constant strain levels of 0.05%, 0.10%, and 0.20%. Both studies discovered that the studied viscoelastic model fits well with the experimental data of the MRE. Despite these previous experimental and numerical modeling studies on the stress relaxation of MREs, detailed quantification of energy and dynamic motion of MREs during shear deformation at the atomic level needs further investigation. Furthermore, to the authors' knowledge, the study of the behavior of MREs subjected to constant strain over small-time scales within picoseconds is still limited. Therefore, conducting stress relaxation studies under small time scales is necessary to depict the changes in energy and rheological behavior of MREs and to avoid the failure of MREs when constant strain is applied.

In the present scenario of advanced computational technology, molecular dynamics (MD) simulation has attracted interest since it offers an “in silico first” approach to optimize the performance of materials in a relatively low-cost environment prior to experimental testing. The MD simulation is also accelerate the innovation process with the capability to predict the properties of modelled elastomers 10 , 11 . In fact, it complements laboratory experimentation with powerful materials informatics such as the glass transition temperatures 12 , mechanical properties 13 , thermodynamics 14 and other physical properties 15 , 16 . From previous studies, using atomistic MD simulation to predict various properties of materials is reliable and simulation results can be used to guide real material design 12 . When performing MD simulation, the choice of ensemble is important to accurately predict and analyze the properties of materials, especially when involving large particles in a modelled system. The ensemble is distinguished by which the variables are held constant throughout the simulation period 17 . For instance, Zhang et al. 18 introduced the NPT (constant number of particles (N), pressure (P), temperature (T)) ensemble through stepwise deformation and relaxation methods, by means of keeping the tensile velocity constant to allow sufficient relaxation in the crosslinked styrene-butadiene rubber model. The study discovered that the integration of both relaxation methods has improved the computational capability when the simulated engineering stress of the model has exceeded one order of magnitude than experimental results. For the shear deformation mode, in a recent study, Ji et al. 19 employed the NVT (constant number of particles (N), volume (V), temperature (T)) ensemble at 600 K with time steps of 50,000 and showed the simulated polymethylmethacrylate filled with silica stored non-bond energy mainly the van der Waals forces of about 95%. Jeong et al. 20 studied the stress relaxation in linear polyethylene and revealed the rheological properties decreased as the overall deformed chain structure become largely relaxed. Another study by Tamir et al. 21 predicted the relaxation modulus of fluoroelastomer using MD simulation and found the relaxation modulus is higher than experimental value. Despite the effort that has been made, the shear mode of the MD simulation in exploring the stress relaxation phenomenon of MRE from the atomic-level perspective is not well-exposed.

This work utilizes the MD simulation method as an additional characterization tool to investigate the energy and molecular dynamics behavior of MRE during the stress relaxation phenomenon. By using the NPT cell ensemble, the basic molecular characteristics behind the stress relaxation phenomena, particularly full energy forms such as stored, potential, and kinetic energies were quantified. The MRE models containing varying magnetic iron particles contents (50–80 wt%) were constructed and energy values were measured. The covalent and non-covalent bond interactions were also quantified. Moreover, the dynamics of the MRE based on radius of gyration and mean square displacement were also explored. The mechanism of stress relaxation based on illustration of particles displacement was studied using the dynamics analysis.

Results and discussion

Determination of linear viscoelastic region of mre from oscillatory shear rheometry.

The strain sweep via oscillatory shear rheometry test was performed to determine the LVE region of MRE. The test was repeated three times to ensure accuracy on MRE samples with 70 and 80 wt% of CIPs. Figure  1 represents a plot of storage modulus ( G' ) as a function of test duration for MRE samples with 70 and 80 wt% CIPs. Using time as the x-axis in Fig.  1 enhances the comprehension of MRE behavior over varying time scales, allowing for comparisons between simulation results and experimental data. This approach is particularly relevant as molecular dynamics (MD) simulations typically produce time series data used to derive properties such as energy. As the shear strain was increased continously from 0.001 to 10%, apparently, the LVE region is present within the strain of 0.001–0.01% in all three samples of MRE with 70 wt% CIPs. During the LVE region, an average G' of 327 kPa was observed for the MRE with 70 wt% CIPs–1,2, and 3 samples. The similar LVE region are also obtained in previous studies 6 , 22 , and this indicates that molecular structure of MREs remains unchanged when this range of strain is applied, as illustrated in the Fig.  1 . Meanwhile, MRE with 80 wt% of CIPs demonstrate shorter LVE region with higher G' ranges from 500 to 552 kPa than MRE with 70 wt% CIPs. This indicates that MRE with 70 wt% of CIPs are able to store energy for longer time than MRE with 80 wt% of CIPs. During the LVE region, the samples did not experience permenant deformation. However, after 80 s, the G' values of MRE began to decrease and finally reached values in the range of 120–199 kPa at final test duration of 134 s, indicating that the energy was starting to dissipate and leads to the breakdown of the MRE molecular chains.

Oscillatory shear rheometry test showing a linear viscoelastic region of MRE samples with 70 and 80 wt% CIPs.

Energy analysis of MRE under stress relaxation through MD simulation

After determination of the LVE region for MRE through experimental method, atomistic MRE models are simulated to a shear process within LVE region (fixed strain of 0.01%) using the MD simulation method. The MRE models are sheared for a total simulation time of 100 ps with 100,000 steps, and their stored energies ( E stored ) are calculated. The E stored can be a good evaluation for the ability of MRE in storing energy that propotionate to the storage modulus, which is one of the rheological properties. In addition, the measurement of E stored provides information about the molecular bond interaction of MRE system from atomistic level. Utilizing time as the x-axis in Figs.  2 and 3 aids in pinpointing critical stages throughout the simulation and enhances the clarity of interpreting stress relaxation phases. The computed E stored of MRE models 1, 2, 3, and 4 with various Fe contents of 50, 60, 70 and 80 wt%, respectively versus simulation time is plotted and shown in Fig.  2 . When the strain of 0.01% is held constant for overall simulation time of 100 ps, it is apparent from Fig.  2 a that the E stored of all MRE models were gradually decreased over time MRE, signifies the strong indication to the stress relaxation phenomenon. Interestingly, the trend of the E stored graph of MRE models is similar to the stress relaxation curve obtained from experimental testing 23 and mathematical modelling 24 .

The stored energy behaviour of simulated MRE models showing ( a ) all stages, ( b ) deformation and ( c ) steady state deformation during stress relaxation phenemonon.

Changes in ( a ) potential energy, ( b ) covalent and non-covalent bonds energies, ( c ) kinetic energy and ( d ) difference in final potential and kinetic energies in the simulated MRE models with various Fe particles content.

Based on the trend of the E stored plot, the stress relaxation phenomenon in MRE can be divided into three main stages, namely the rapid stress relaxation (stage 1), stabilization and deformation (stage 2) and stable deformation stage (stage 3). During stage 1, the E stored of MRE models decreases rapidly from the initial E stored . This rapid stress relaxation stage is completed within approximately 0.3 ps in all models from the beginning of simulation time. This stage is also found in other previous studies 25 , 26 . It is also noticeable that the initial E stored of MRE is higher when more Fe particles are added into SR, with the highest initial E stored (25,289 kJ) for the MRE model 4. Although the simulated MRE model with 80 wt% Fe particles causes a relatively high initial E stored , this model exhibits a high relaxation decrease in E stored (32%) to 17,000 kJ by the end of stage 1, indicating a low ability to store energy within this time range. The similar finding is observed in previous rheological test that revealed 80 wt% CIPs have high storage modulus but it is a brittle sample because the presence of short LVE region 22 . It was also previously reported that increasing SiO 2 loading in natural rubber causes a substantial decrease in stress relaxation due to the more SiO 2 leads to progressive breakdown of the filler aggregates and causes the polymer chains get desorbed from the filler surface 27 .

After the rapid stress relaxation stage, MRE models enters the stabilization and deformation stage as simulation time elapses after 0.3 ps. This region is called stabilization and deformation because the molecules in MRE model experience a steady-state increase in E stored until the simulation time reaches 3 ps and followed by particles deformation by the half of simulation time of stage 2 (red dotted box (b)). The deformation stage starts approximately after 10% of the total simulation time. During stage 2, the E stored pattern suggests that after rapid stress relaxation, the particles stabilizes to achieve stable deformation stage. In previous study, this is called physical relaxation mechanism that involves the rearranging of molecular chains towards new configuration in equilibirium at the new strained state 23 . It is noteworthy the higher onset deformation is observed with increasing Fe particles, for example model 4 deforms slower than model 2 (Fig.  2 b). Previous study 28 found that 70 wt% of CIPs has increased the storage modulus in silicone rubber matrix than 60 wt% of CIPs. Hence, stiffer MRE needs longer time to deform and eventually increases onset deformation. Furthermore, beyond 60 ps of the total simulation time, the E stored of all MRE models gradually decreases and reaches stable deformation stage (red dotted box (c)), suggesting the completion of the stress relaxation process. It is noticeable that there is insignificant difference for E stored during this steady state deformation, as shown in Fig.  2 c, indicating that the internal molecular response of MRE and external strain (0.01%) achieve equilibrium state.

Table 1 shows the stored energy evolution of MRE models over simulation time. An increase in E stored difference ranging from 8.63% to 52.37% is observed in all MRE models. This observation signifies the effect of Fe particles on the stress relaxation phenomenon in MRE, in which greater particles contents induce higher E stored difference. For example, model 3 with 70 wt% Fe particles induces a decrease in E stored of about 21.42% after the simulation. Note there is a systematic discrepancy of the stress relaxation experiment 5 in which the storage modulus of MRE with 70 wt% of CIPs decreased by about 0.5% by the end of the test duration compared to the simulation result. Previous study 29 mentioned that quantitative comparisons between MD simulations and experiments may offer discrepancy due to differences in length and time scales. In this work, the discrepancy is due to the time used during the simulation is within small scale (1 × 10 −10  s).

In contrast to the experimental approach, utilizing MD simulation provides an additional quantitative tool for assessing the time-dependent effect of stored energy of MRE model during stress relaxation. In the present study, the important point is decreasing trend of stored energy over time, indicating the occurrence of stress relaxation phenomenon within the LVE region of MRE. Therefore, the MD simulation emerges as a promising computational method and contributes to an understanding of the changes in stored energy in MRE samples during stress relaxation from atomic level.

It is reasonable to expect that the stress relaxation phenomenon in MRE is a consequence of its specific atomic structure. Based on this idea, various forms of energy of MRE models under the stress relaxation are calculated and presented in Fig.  3 . Variations of potential energy ( E potential ) of MRE models over increasing simulation time is presented in Fig.  3 a. The E potential of a simulated model is a sum of intramolecular potentials (covalent bond) and intermolecular potentials (non-covalent bond). Apparently, the E potential showed a gradual decrease over simulation time. The trend of E potential resembles the trend of E stored (Fig.  2 a, suggesting the stress relaxation phenomenon is largely contributed by the change in potential energy of atoms in MRE models. It is also observed that the final in potential energy (final E stored ) increased as the Fe particles contents increased, as shown in the inset of Fig.  3 a. While the shear deformation of all MRE models occurs after the initial 0.1 ps, it is interesting to observe the higher final E potential (> 2000 kJ) in MRE model 2–4 compared to model 1, suggesting that > 50 wt% of Fe particles causes higher intramolecular and intermolecular potentials.

To further understand, the components of E potential of elements in MRE model such as the covalent bond and non-covalent bond interactions are calculated and presented in Fig.  3 b. The covalent bond interaction is composed of energies of bond stretching, angle bending and dihedral torsion between atoms, while the non-covalent bond is the van der Waals and columbic interactions 30 , 31 . Evidently, covalent bond energy is higher than the non-covalent bond energy in all MRE models, suggesting that the attraction between covalently bonded atoms are much higher than the short range van der Waals forces. The bond energy (2492–2157 kJ) and angle energy (3942–3403 kJ) are higher than torsion energy (590–417 kJ) of atoms in all MRE models because breaking covalent bond require more energy compared to relatively lower energy required for torsional rotation of each bond.

Table 2 shows the values of various energy of MRE models. The highest final E potential (3262 kJ) of MRE model 4 is mainly contributed by the covalent bond interactions that includes the bond (2157 kJ), angle (3403 kJ), torsion (417 kJ) energies compared to weak van der Waals energy (− 2717 kJ) and columbic energy (2 kJ). This explains the slower deformation of E stored model 4, as previously discussed. Furthermore, the change in E potential of the elements in MRE models also is largely affected by the van der Waals energy, as seen increases with increasing Fe particles. The stronger van der Waals energy in MRE model 3 (− 2697 kJ) and model 4 (− 2717 kJ) than model 1 (− 5187 kJ) suggest that there is a strengthening of van der Waals interactions with addition of 70 and 80 wt% of Fe particles.

The increase in van der Waals energy in MRE model 3 signifies an increase in the attractive forces between MRE molecules due to shear-induced changes in molecular proximity. To elaborate further, the shear forces can bring MRE molecules closer together and alter their orientations, leading to increased contact between them. When more Fe particles are present, the enhanced proximity between Fe, SR and VTMS molecules can result in stronger van der Waals energy probably due to greater overlap of electron clouds. Therefore, the stronger van der Waals energy can promote tighter packing of molecules and breaking of the bonds in these MRE models become hard and results in higher onset deformation. This observation is also described in previous study 32 that 80 wt% of CIPs has more tendency to form aggregates than MRE with low CIPs content.

Figure  3 c shows the kinetic energy ( E kinetic ) of all MRE models. The E kinetic seems to be consistent over simulation time because the temperature of the system is homologous (T = 25 °C) throughout the entire shear simulation. The almost-consistent E kinetic also indicates the structural stability of MRE models during the stress relaxation phenomenon. Previous study demonstrated that the entanglement of molecular chains in the amorphous system improved the structural stability 33 . An interesting observation is that particles in MRE model 2, 3, and 4 exhibit lower E kinetic than model 1. For instance, MRE model 3 exhibit a lower E kinetic (9127 kJ) compared model 1 (9717 kJ). The decrease of the E kinetic of model 3 by approximately 6% is presumably due to the increased final potential energy (2983 kJ) caused by non-covalent bond interactions of van der Waals energy (− 2697.02) when more Fe particles are introduced. Therefore, the mobility of molecules in MRE models are more restricted and results in low kinetic energy in model with high Fe particles contents.

Variations of final E potential and E kinetic of MRE models with various Fe particles contents are presented in Fig.  3 d. The observation is apparent in which the trend of final E potential and E kinetic alternates as the final E potential increases and final E kinetic decreases with an increase in Fe particle contents. This indicates that stronger intramolecular and intermolecular interactions, attributed to higher Fe particles contents and hence, increase the potential energy of MRE model. Consequently, the increased potential energy constrain the movement of MRE particles during stress relaxation phenomenon, and therefore decrease the kinetic energy of particles.

Dynamics behaviour of MRE under stress relaxation through MD simulation

The dynamics analysis of MRE was studied with an aim to elucidate the molecular behaviour of MRE from the atomic level perspective. In MD simulations, the displacement of particles is a fundamental aspect and it involves modelling the motion of particles. Figure  4 presents an illustration of MRE models in 3D simulation space during the stress relaxation. When the simulation time starts at 0 s, it is observable that molecules of Fe, SR and VTMS still adhere to the wall of the simulation boxes. This illustrates the non displacement of particles during the initial simulation time.

Illustration of displacement of particles in the MRE models ( a ) 1–50 wt%, ( b ) 2–60 wt%, ( c ) 3–70 wt% and ( d ) 4–80 wt% of Fe particles during the stress relaxation.

By the end of simulation time (t = 100 ps), it is noticeable that the cluster of Fe particles are displaced into largely-separated Fe atoms that move outside the simulation box. The detachment of Fe atoms away from SR molecules in all MRE models, as shown in Fig.  4 a–d represents the shearing of Fe particles during the stress relaxation. It is also apparent that the large cluster of SR molecules has been divided into pieces in MRE model with the highest Fe content (80 wt%), indicating that the matrix particles (SR) has been sheared during the stress relaxation. The shearing of the SR matrix prevents energy from being stored, causing it to instead dissipate into the surrounding atoms. This theoretical finding is supported by previous experimental study that discovered the reduction of matrix elasticity as a result to the formation of shear band during the stress relaxation 5 . Therefore, through these illustration, it is interesting to visualise the change in displacement of particles in MRE from the atomistic perspective using the MD simulation.

The radial distribution function (RDF) values shows a specific peak at a distance r in a simulated model. As shown in Fig.  5 , there are few peaks present at different distance, the highest peak is located in the range of 1.0–1.1 Å, that represents chemical bonds and hydrogen bonds 14 . It can be observed that Model 4 has the highest intensity compared to other models, as shown in the inset of Fig.  5 . This suggests that MRE model 4 with 80 wt% Fe particles exhibit stronger intramolecular and intermolecular bondings than other Fe particles contents.

Radial distribution function values of MRE models.

The mean square displacement (MSD) represents the mobility of molecules from an initial simulation until end of simulation time 34 . MSD also is a measure of average energy particles have moved from their initial positions over a given time interval 14 . Figure  6 shows the MSD curves for all MRE models as a function of simulation time. The MSD values increases with increasing simulation time, indicating the MRE particles are moving when the stress relaxation occurs. Notably, the final MSD value increased with decreasing Fe particles contents. This MSD result is similar with previous study 35 that revealed increasing additive contents to phenyl silicone rubber causes a decrease of mobility of rubber chains.

Mean square displacement curves of MRE models.

The MRE model 1 exhibit the highest final MSD value of 45,476 Å at 100 ps, indicating more extensive particle movement over time. This result corroborates with high final kinetic energy of MRE model 1 (9717 kJ). This suggests the MRE model with 50 wt% of Fe particles with higher kinetic energy tend to move freely during stress relaxation. Comparatively, the MSD of MRE model 4 exhibit the lowest final MSD value of 20,318 Å 2 . In fact, by the end of simulation time, the final MSD of MRE model 4 decreased about 30% than that model 1.This indicates the addition of 80 wt% of Fe particles results in hindered mobility of MRE chains and MRE particles are not moving much from their initial positions during the shear process. This result also agrees with its low final kinetic energy (9362 kJ). Another previous studies 36 , 37 mentioned that limited mobility of rubber chains is likely due to the added particles acting as obstacles. In this work, higher Fe particles content hinders the mobility of molecular chains during shear process, and hence, lower MSD values in MRE models.

Experimental

Material and preparation of mres.

Silicone rubber (SR) type RTV-A NS625 in the form of viscous white liquid having density of 1.08 g/cm 3 and viscosity of 18 ± 2 Pa s at 25 °C was supplied by Nippon Steel Corporation, Tokyo, Japan and used as the MRE matrix. The spherical carbonyl iron particles (CIPs) (BASF Corporation, Ludwigshafen, Germany) with the produce code of carbonyl iron powder OM grade (Number 51258195) and an average diameter of 4 μm, was used as magnetic particles. The MRE samples were prepared according to the formulation of 70:30 ratio, in which 70 wt% of CIPs was added to 30 wt% of SR. This ratio is selected based on the previous study 6 that found 70 wt% of CIPs is the optimum content for the improvement in the rheological properties of MREs. The SR and CIPs were homogenously mixed thoroughly using a mechanical stirrer (WiseStir HT-DX, PMI-Labortechnik GmbH, Switzerland) at a stirring speed of 200 rpm for 30 min. Immediately after 30 min, vinyltrimethoxysilane (VTMS) curing agent (Nippon Steel Corporation, Tokyo, Japan) was added into the mixture in 1.5 wt% and stirred rigorously for another 2 min. The resulting mixture was then cast over a rectangular mold and allowed to cure at room temperature for four hours to form a 1 mm thick MRE sheet. The sheet was dried and stored in desiccator prior to testing.

Experimental oscillatory shear rheometry test

For the determination of LVE region, the oscillatory shear rheometry test was performed. The MRE samples were prepared by cutting the MRE sheet into MRE circular samples having diameter of 20 mm and thickness of 1 mm, by using hollow hole punch tool. The storage modulus measurement was performed using an oscillation parallel plate rheometer (MCR 302 Anton Paar, Austria). The temperature control device (Viscotherm VT2, Anton Paar, Austria) was utilized for controlling the measuring temperature to be at 25 °C. The parallel plate (PP20) was suitably selected according to the dimension of the MRE samples (20 mm diameter). The MRE sample was centrally placed between the top rotary and bottom parallel plates of the rheometer. In this study, an oscillatory shear rheometry test mode under constant frequency (1 Hz) was used for entire experiment. The strain amplitude sweep was performed in order to measure the storage modulus that is proportionate to the stored energy within viscoelastic materials during the oscillatory shear rheometer. For the strain amplitude sweep, the shear strain was increased continuously from 0.001 to 10% throughout the test with an interval of 30 points and the total duration of the test was set to 150 s. The oscillatory shear rheometer was repeated for three times to get an average result.

Model and simulation details

The MD simulation was performed using Dassault Systemes BIOVIA Materials Studio software. Generally, the MD simulation comprises of three stages which are the construction of model, equilibration, and production steps. For the first step (construction of model), the silicone rubber (SR), magnetic iron (Fe) particles and vinyltrimethoxysilane (VTMS) molecules were modelled using the Materials Visualizer within the software. The SR, Fe particles and VTMS molecules were built based on their chemical structures. All molecules underwent the geometry optimization process. Having modelled all the molecules, the final step in constructing a model for subsequent simulation is defining the periodic simulation box. For this purpose, the Fe particles and VTMS molecules were randomly distributed in the SR system, according to weight percentage (wt%), as listed in Table 3 . Figure  7 presents the three-dimensional (3D) simulation box that represents the MRE models with 50, 60, 70, and 80 wt% of Fe particles, that labelled as model 1, 2, 3, and 4, respectively. The size of magnetic iron particles in MD simulation is about 10 nm. All models were constructed using the Amorphous Cell construction module. The simulation box dimensions for the MRE models were set as 35.3 × 35.3 × 35.3 Å 3 .

Models for MD simulation of MREs (grey, red, white, purple and yellow spheres represent C, O, H, Fe and Si atoms, respectively).

After model construction, an equilibration step involving an energy minimization module was performed to equilibrate this molecular system. For this step, the MRE model was integrated under the NVT canonical ensemble at 25 °C to let the molecules to relax and achieve a zero initial stress state at this particular temperature. The energy convergence threshold was set to minimum energy of 0.001 kcal/mol, and total simulation steps of 100,000 with the time step of 1 femtosecond (fs) were employed. A short time step (1 fs) is required to ensure numerical stability. The final MRE model was used for subsequent molecular simulation.

The production step, which is the shear simulation, was performed using the Forcite shear module. Figure  8 shows the flowchart of approach taken for the shear simulation method. In general, the shear simulation mimics the experiment in which the material is placed between two plates and then sheared according to the choice of the shear direction. The velocity profile of the molecular system can be generated by sliding the upper and lower walls in either left and right directions 38 . Some key parameters of the module were determined before the simulation. In this work, the choice of NPT ensemble was selected because this ensemble can conserve constant particles at a constant temperature. The forcefield energy was set to universal, with the charges of the molecules were set to current. Moreover, the timestep of 1 fs was selected and total simulation steps was set to 100,000 during the simulation to ensure accurate data are obtained. The frame output was obtained every 100 steps during simulation. Furthermore, the Ewald summation method was used for calculating electrostatic interaction with accuracy level of 0.001 kcal/mol with the buffer width of 0.5 Å. The atom-based summation method for Van der Waals forces with the truncation method of cubic spline with the buffer width of 0.5 Å were selected. Other key parameters such as the shear strain of 0.01% and simulation temperature of 25 °C, were fixed throughout the entire shear simulation. Following the shear simulation setup, the MRE model was selected as the input. The shear simulation was performed on each model according to the fixed setup. The shear direction (plane) was specified to be at plane B (top) of the simulation cell to mimic the movement of the top rotary plate of the rheometer. In the rheology of viscoelastic materials, the stored energy during deformation is proportional to the shear storage modulus, that can be expressed as the following Eq. ( 1 ) 39 , 40 :

where E s is the stored energy, G′ is the shear storage modulus and γ o is the strain amplitude.

Overall flowchart of the MD simulation method in characterizing energy and dynamics behaviour of MRE models.

The stored energy of the MRE model was calculated as the sum of potential and kinetic energies (i.e., the SR matrix phase and Fe particles phase) as shown in Eq. ( 2 ):

where E stored represents the stored energy that is equivalent to total energy, E potential and E kinetic represent the potential energy and kinetic energy of the simulated MRE system, respectively.

The potential energy of the MRE model was calculated as the sum of intramolecular and intermolecular potentials, as shown in Eq. ( 3 ):

where E bond , E angle , E torsion , represents the intramolecular potentials which are the bond energy, angle energy, torsion energy, respectively. The intermolecular potentials are represented by the van der Waals energy ( E van der Waals ) and columbic energy ( E columbic ) of the simulated MRE models.

The kinetic energy of the MRE model was calculated using the classical mechanics formula as shown in Eq. ( 4 ):

where N is the total number of particles, m i is the mass of the i -th particle, v i is the velocity vector of the i -th particle.

After running simulation under the shear deformation mode, if the simulation results show the stress relaxation phenomenon, which is in this study, the gradual decrease of stored energy over simulation time, the dynamics of the simulated model was then characterized using the Forcite Analysis module. The determination of mean square displacement (MSD) values of the simulated model was calculated according to the trajectory results after simulation by using Eq. ( 5 ):

where r (t) and r (0) represent position of the mass center for the molecule at time t and 0, respectively.

Another information obtained from the dynamics analysis is the radial distribution function (RDF), which is a tool to characterize the molecular structure that evaluates the relative probability of finding a particle at a distance r from the reference position (g(r)).

In this investigation, the MD simulation was employed to investigate energy and dynamics behavior of MRE during stress relaxation. The experimental shear rheometer showed that the linear viscoelastic region of MRE with 70 wt% CIPs is within 0.001–0.01% of strain. Furthermore, the stored energy of all MRE models MRE models containing 50–80 wt% of Fe particles decreased over time, demonstrating that the stress relaxation can still occur within the LVE region of MRE. During stress relaxation, the potential energy of particles in all MRE models decreased over time, due to the change in covalent bond interactions, van der Waals and Columbic interactions. Notably, the high final E stored in the MRE model with 80 wt% of Fe particles is due to the increased intramolecular and intermolecular interactions. Furthermore, the mobility of this MRE model also decreased, as shown by the lowest final MSD value (20,318 Å 2 ). The results indicate that MD simulation proves to be a promising quantitative tool for comprehending the alterations in energy and dynamics behavior exhibited by MRE during stress relaxation. This study is advantageous for examining stress relaxation from an atomic level perspective and for advancing the development of MRE in the field of nanotechnology.

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

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Acknowledgements

The authors acknowledge the financial support provided by UTM Fundamental Research (Vot No. 22H14) and Professional Development Research University (PDRU) (Vot. No. 06E95). Author M.S. wishes to thank the Czech Science Foundation [23-07244S] for the financial support.

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Nurul Hakimah Lazim, Mohd Aidy Faizal Johari, Saiful Amri Mazlan, Nur Azmah Nordin & Shahir Mohd Yusuf

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N.H.L. conducted the experiments and simulations, analysed the data, prepared the figures and wrote the main manuscript, while S.A.M. and M.S. supervised the entire practical work and reviewed the manuscript. M.A.F.J., N.A.N., and S.M.Y. reviewed the manuscript.

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Lazim, N.H., Johari, M.A.F., Mazlan, S.A. et al. Molecular dynamics and experimental analysis of energy behavior during stress relaxation in magnetorheological elastomers. Sci Rep 14 , 19724 (2024). https://doi.org/10.1038/s41598-024-70459-7

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Received : 20 May 2024

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Published : 25 August 2024

DOI : https://doi.org/10.1038/s41598-024-70459-7

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