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experimental unit

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experimental unit , in an experimental study, a physical entity that is the primary unit of interest in a specific research objective. Generally, the experimental unit is the person, animal, or object that is the subject of the experiment. Experimental units receive different treatments from one another in an experiment.

As a case in point, consider an experiment designed to determine the effect of three different exercise programs on the cholesterol level of patients with elevated cholesterol. Each patient is referred to as an experimental unit, the response variable is the cholesterol level of the patient at the completion of the program, and the exercise program is the factor whose effect on cholesterol level is being investigated. Each of the three exercise programs is referred to as a treatment .

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1.1 - cases & variables.

Throughout the course, we will be using many of the terms introduced in this lesson. Let's start by defining some of the most frequently used terms: case, variable, and constant.

A  case  is an experimental unit. These are the individuals from which data are collected. When data are collected from humans, we sometimes call them  participants . When data are collected from animals, the term  subjects  is often used. Another synonym is  experimental unit . 

A  variable  is a characteristic that is measured and can take on different values. In other words, something that varies between cases. This is in contrast to a constant  which is the same for all cases in a research study.

Let's look at a few examples.

Example: Study Time & Grades Section  

A teacher wants to know if third grade students who spend more time reading at home get higher homework and exam grades.

The students are the  cases . There are three  variables : amount of time spent reading at home, homework grades, and exam grades. The grade-level of the students is a  constant  because all students are in the third grade.

Example: Dog Food Section  

A researcher wants to know if dogs who are fed only canned food have different body mass indexes (BMI) than dogs who are fed only hard food. They collect BMI data from 50 dogs who eat only canned food and 50 dogs who eat only hard food.

The  cases  are the dogs. There are two  variables : type of food and BMI. A  constant  would be subspecies, because all cases are domestic dogs.

Example: Age & Weight of Sea Otters Section  

Researchers are studying the relationship between age and weight in a sample of 100 male sea otters ( Enhydra lutris ).

The 100 otters are the  cases . There are two  variables : age and weight. Biological sex is a  constant  because all subjects are male. Species is also a  constant . 

1.4 Experimental Design and Ethics

Does aspirin reduce the risk of heart attacks? Is one brand of fertilizer more effective at growing roses than another? Is fatigue as dangerous to a driver as the influence of alcohol? Questions like these are answered using randomized experiments. In this module, you will learn important aspects of experimental design. Proper study design ensures the production of reliable, accurate data.

The purpose of an experiment is to investigate the relationship between two variables. When one variable causes change in another, we call the first variable the explanatory variable . The affected variable is called the response variable . In a randomized experiment, the researcher manipulates values of the explanatory variable and measures the resulting changes in the response variable. The different values of the explanatory variable are called treatments . An experimental unit is a single object or individual to be measured.

You want to investigate the effectiveness of vitamin E in preventing disease. You recruit a group of subjects and ask them if they regularly take vitamin E. You notice that the subjects who take vitamin E exhibit better health on average than those who do not. Does this prove that vitamin E is effective in disease prevention? It does not. There are many differences between the two groups compared in addition to vitamin E consumption. People who take vitamin E regularly often take other steps to improve their health: exercise, diet, other vitamin supplements, choosing not to smoke. Any one of these factors could be influencing health. As described, this study does not prove that vitamin E is the key to disease prevention.

Additional variables that can cloud a study are called lurking variables . In order to prove that the explanatory variable is causing a change in the response variable, it is necessary to isolate the explanatory variable. The researcher must design her experiment in such a way that there is only one difference between groups being compared: the planned treatments. This is accomplished by the random assignment of experimental units to treatment groups. When subjects are assigned treatments randomly, all of the potential lurking variables are spread equally among the groups. At this point the only difference between groups is the one imposed by the researcher. Different outcomes measured in the response variable, therefore, must be a direct result of the different treatments. In this way, an experiment can prove a cause-and-effect connection between the explanatory and response variables.

The power of suggestion can have an important influence on the outcome of an experiment. Studies have shown that the expectation of the study participant can be as important as the actual medication. In one study of performance-enhancing drugs, researchers noted:

Results showed that believing one had taken the substance resulted in [ performance ] times almost as fast as those associated with consuming the drug itself. In contrast, taking the drug without knowledge yielded no significant performance increment. 1

When participation in a study prompts a physical response from a participant, it is difficult to isolate the effects of the explanatory variable. To counter the power of suggestion, researchers set aside one treatment group as a control group . This group is given a placebo treatment–a treatment that cannot influence the response variable. The control group helps researchers balance the effects of being in an experiment with the effects of the active treatments. Of course, if you are participating in a study and you know that you are receiving a pill which contains no actual medication, then the power of suggestion is no longer a factor. Blinding or masking in a randomized experiment preserves the power of suggestion. When a person involved in a research study is blinded, they do not know who is receiving the active treatment(s) and who is receiving the placebo treatment. A double-blind experiment is one in which both the subjects and the researchers involved with the subjects are blinded.

Example 1.19

Researchers want to investigate whether taking aspirin regularly reduces the risk of heart attack. Four hundred people between the ages of 50 and 84 are recruited as participants. The people are divided randomly into two groups: one group will take aspirin, and the other group will take a placebo. Each person takes one pill each day for three years, but they don't know whether they are taking aspirin or the placebo. At the end of the study, researchers count the number of people in each group who have had heart attacks.

Identify the following values for this study: population, sample, experimental units, explanatory variable, response variable, treatments.

The population is people aged 50 to 84. The sample is the 400 people who participated. The experimental units are the individual people in the study. The explanatory variable is oral medication. The treatments are aspirin and a placebo. The response variable is whether a subject had a heart attack.

Try It 1.19

A study needs to be conducted of the effect of three medicines A, B, and C on the height of adults aged 30 to 45. 90 adults were selected randomly and divided into three equal groups. The first group was asked to take medicine A for 6 months. The second group was asked to take medicine B for 6 months. The third group was asked to take medicine C for 6 months. The average change in height in each group is calculated at the end of the study.

Identify the following values for this study: population, sample, experimental units, explanatory variables, response variable, treatments.

Example 1.20

The Smell & Taste Treatment and Research Foundation conducted a study to investigate whether smell can affect learning. Subjects completed mazes multiple times while wearing masks. They completed the pencil and paper mazes three times wearing floral-scented masks, and three times with unscented masks. Participants were assigned at random to wear the floral mask during the first three trials or during the last three trials. For each trial, researchers recorded the time it took to complete the maze and the subject’s impression of the mask’s scent: positive, negative, or neutral.

• Describe the explanatory and response variables in this study.
• What are the treatments?
• Identify any lurking variables that could interfere with this study.
• Is it possible to use blinding in this study?
• The explanatory variable is scent, and the response variable is the time it takes to complete the maze.
• There are two treatments: a floral-scented mask and an unscented mask.
• All subjects experienced both treatments. The order of treatments was randomly assigned so there were no differences between the treatment groups. Random assignment eliminates the problem of lurking variables.
• Subjects will clearly know whether they can smell flowers or not, so subjects cannot be blinded in this study. Researchers timing the mazes can be blinded, though. The researcher who is observing a subject will not know which mask is being worn.

Try It 1.20

The Placebo Research Group conducted a study to find the extent of placebo effects. A group of men randomly selected were asked to take a test before and after taking a pill that induces a mild headache. The pill in half of the randomly selected men was replaced with a similar pill that has no effect. For each trial, researchers recorded the change in time men took to complete the tests before and after taking the pill.

• Describe the explanatory and response variable in this study.

Example 1.21

A researcher wants to study the effects of birth order on personality. Explain why this study could not be conducted as a randomized experiment. What is the main problem in a study that cannot be designed as a randomized experiment?

The explanatory variable is birth order. You cannot randomly assign a person’s birth order. Random assignment eliminates the impact of lurking variables. When you cannot assign subjects to treatment groups at random, there will be differences between the groups other than the explanatory variable.

Try It 1.21

You are concerned about the effects of texting on driving performance. Design a study to test the response time of drivers while texting and while driving only. How many seconds does it take for a driver to respond when a leading car hits the brakes?

• Describe the explanatory and response variables in the study.
• What should you consider when selecting participants?
• Your research partner wants to divide participants randomly into two groups: one to drive without distraction and one to text and drive simultaneously. Is this a good idea? Why or why not?
• How can blinding be used in this study?

The widespread misuse and misrepresentation of statistical information often gives the field a bad name. Some say that “numbers don’t lie,” but the people who use numbers to support their claims often do.

An investigation of famous social psychologist, Diederik Stapel, has led to the retraction of his articles from some of the world’s top journals including Journal of Experimental Social Psychology, Social Psychology, Basic and Applied Social Psychology, British Journal of Social Psychology, and the magazine Science . Diederik Stapel is a former professor at Tilburg University in the Netherlands. An extensive investigation involving three universities where Stapel has worked concluded that the psychologist is guilty of fraud on a colossal scale. Falsified data taints over 55 papers he authored and 10 Ph.D. dissertations that he supervised.

Stapel did not deny that his deceit was driven by ambition. But it was more complicated than that, he told me. He insisted that he loved social psychology but had been frustrated by the messiness of experimental data, which rarely led to clear conclusions. His lifelong obsession with elegance and order, he said, led him to concoct sexy results that journals found attractive. “It was a quest for aesthetics, for beauty—instead of the truth,” he said. He described his behavior as an addiction that drove him to carry out acts of increasingly daring fraud, like a junkie seeking a bigger and better high. 2

The committee investigating Stapel concluded that he is guilty of several practices including:

• creating datasets, which largely confirmed the prior expectations,
• altering data in existing datasets,
• changing measuring instruments without reporting the change, and
• misrepresenting the number of experimental subjects.

Clearly, it is never acceptable to falsify data the way this researcher did. Sometimes, however, violations of ethics are not as easy to spot.

Researchers have a responsibility to verify that proper methods are being followed. The report describing the investigation of Stapel’s fraud states that, “statistical flaws frequently revealed a lack of familiarity with elementary statistics.” 3 Many of Stapel’s co-authors should have spotted irregularities in his data. Unfortunately, they did not know very much about statistical analysis, and they simply trusted that he was collecting and reporting data properly.

Many types of statistical fraud are difficult to spot. Some researchers simply stop collecting data once they have just enough to prove what they had hoped to prove. They don’t want to take the chance that a more extensive study would complicate their lives by producing data contradicting their hypothesis.

Professional organizations, like the American Statistical Association, clearly define expectations for researchers. There are even laws in the federal code about the use of research data.

When a statistical study uses human participants, as in medical studies, both ethics and the law dictate that researchers should be mindful of the safety of their research subjects. The U.S. Department of Health and Human Services oversees federal regulations of research studies with the aim of protecting participants. When a university or other research institution engages in research, it must ensure the safety of all human subjects. For this reason, research institutions establish oversight committees known as Institutional Review Boards (IRB) . All planned studies must be approved in advance by the IRB. Key protections that are mandated by law include the following:

• Risks to participants must be minimized and reasonable with respect to projected benefits.
• Participants must give informed consent . This means that the risks of participation must be clearly explained to the subjects of the study. Subjects must consent in writing, and researchers are required to keep documentation of their consent.
• Data collected from individuals must be guarded carefully to protect their privacy.

These ideas may seem fundamental, but they can be very difficult to verify in practice. Is removing a participant’s name from the data record sufficient to protect privacy? Perhaps the person’s identity could be discovered from the data that remains. What happens if the study does not proceed as planned and risks arise that were not anticipated? When is informed consent really necessary? Suppose your doctor wants a blood sample to check your cholesterol level. Once the sample has been tested, you expect the lab to dispose of the remaining blood. At that point the blood becomes biological waste. Does a researcher have the right to take it for use in a study?

It is important that students of statistics take time to consider the ethical questions that arise in statistical studies. How prevalent is fraud in statistical studies? You might be surprised—and disappointed. There is a website dedicated to cataloging retractions of study articles that have been proven fraudulent. A quick glance will show that the misuse of statistics is a bigger problem than most people realize.

Vigilance against fraud requires knowledge. Learning the basic theory of statistics will empower you to analyze statistical studies critically.

Example 1.22

Describe the unethical behavior in each example and describe how it could impact the reliability of the resulting data. Explain how the problem should be corrected.

A researcher is collecting data in a community.

• The researcher selects a block where they are comfortable walking because they know many of the people living on the street.
• No one seems to be home at four houses on the route. They do not record the addresses and do not return at a later time to try to find residents at home.
• The researcher skips four houses on the route because they are running late for an appointment. When they get home, they fill in the forms by selecting random answers from other residents in the neighborhood.
• By selecting a convenient sample, the researcher is intentionally selecting a sample that could be biased. Claiming that this sample represents the community is misleading. The researcher needs to select areas in the community at random.
• Intentionally omitting relevant data will create bias in the sample. Suppose the researcher is gathering information about jobs and child care. By ignoring people who are not home, They may be missing data from working families that are relevant to her study. They need to make every effort to interview all members of the target sample.
• It is never acceptable to fake data. Even though the responses the researcher are “real” responses provided by other participants, the duplication is fraudulent and can create bias in the data. They researcher needs to work diligently to interview everyone on their route.

Try It 1.22

Describe the unethical behavior, if any, in each example and describe how it could impact the reliability of the resulting data. Explain how the problem should be corrected.

A study is commissioned to determine the favorite brand of fruit juice among teens in California.

• The survey is commissioned by the seller of a popular brand of apple juice.
• There are only two types of juice included in the study: apple juice and cranberry juice.
• Researchers allow participants to see the brand of juice as samples are poured for a taste test.
• Twenty-five percent of participants prefer Brand X, 33% prefer Brand Y and 42% have no preference between the two brands. Brand X references the study in a commercial saying “Most teens like Brand X as much as or more than Brand Y.”
• 1 McClung, M. Collins, D. “Because I know it will!”: placebo effects of an ergogenic aid on athletic performance. Journal of Sport & Exercise Psychology. 2007 Jun. 29(3):382-94. Web. April 30, 2013.
• 2 Yudhijit Bhattacharjee, “The Mind of a Con Man,” Magazine, New York Times, April 26, 2013. Available online at: http://www.nytimes.com/2013/04/28/magazine/diederik-stapels-audacious-academic-fraud.html?src=dayp&_r=2& (accessed May 1, 2013).
• 3 “Flawed Science: The Fraudulent Research Practices of Social Psychologist Diederik Stapel,” Tillburg University, November 28, 2012, http://www.tilburguniversity.edu/upload/064a10cd-bce5-4385-b9ff-05b840caeae6_120695_Rapp_nov_2012_UK_web.pdf (accessed May 1, 2013).

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Note that this "residual" for the within plot \(subplot\) part of the analysis is actually the sum of squares for the interaction of rows \(w\ hole plots\) with varieties \(subplot treatments\)---as in an RCBD.

- r_k\(i\) ~ N\(0, sigma^2_r\)

- e_ijk ~ N\(0, sigma^2_e\)

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• > Statistical Principles for the Design of Experiments
• > Experimental units

Book contents

• Frontmatter
• Part I Overture
• Part II First subject
• 5 Experimental units
• 6 Replication
• 7 Blocking and control
• 8 Multiple blocking systems and cross-over designs
• 9 Multiple levels of information
• 10 Randomisation
• 11 Restricted randomisation
• Part III Second subject
• Part IV Coda

5 - Experimental units

from Part II - First subject

Published online by Cambridge University Press:  05 November 2012

Preliminary examples

( a ) Gene expression studies using spotted microarray technologies allow the comparison of gene transcription responses for different experimental samples, such as plant samples taken from different plant lines (a wild-type and lines with different genetic mutations), having been exposed to different environmental conditions or inoculated with a pathogen, and possibly collected at different times after exposure or incoluation. Each microarray contains probes (spots) for a large number (many thousands) of genes, with these probes arranged in a rectangular grid within the microarray. Some microarray technologies only allow one sample to be hybridised to each array, but others (multichannel systems) allow a mixture of two (or more) samples to be hybridised to the array, with the samples being differentially labelled (using fluorescent dyes) prior to being mixed, and separate responses being measured for each of the fluorescent labels. Scientific interest is in both the patterns of gene expression measured for each probe across experimental samples, and in the relationships between gene expression responses measured for different probes within and between experimental samples. For multichannel systems, generally each combination of array and channel might be considered as the experimental unit, though considering the probe (gene) as a ‘treatment’ (as some analysis approaches do) suggests that each spot should be considered as the experimental unit. An added complication in most gene expression microarray studies is that the experimental samples will have been obtained from a field, glasshouse or controlled environment experiment, so that the design of this earlier experiment, and the various processing steps between initial experimental sample and microarray sample, should be considered in determining the structure of the microarray experiment. Similar issues arise with other ‘high throughput’ technologies used in molecular biology studies.

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• Experimental units
• R. Mead , University of Reading , S. G. Gilmour , University of Southampton , A. Mead , University of Warwick
• Book: Statistical Principles for the Design of Experiments
• Online publication: 05 November 2012
• Chapter DOI: https://doi.org/10.1017/CBO9781139020879.006

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1.4 Designed Experiments

Observational studies vs. experiments.

Ignoring anecdotal evidence, there are two primary types of data collection: observational studies and controlled (designed) experiments .  Remember, we typically cannot make claims of causality from observation studies because of the potential presence of confounding factors.  However, making causal conclusions based on experiments is often reasonable by controlling for those factors. Consider the following example:

Suppose you want to investigate the effectiveness of vitamin D in preventing disease. You recruit a group of subjects and ask them if they regularly take vitamin D. You notice that the subjects who take vitamin D exhibit better health on average than those who do not. Does this prove that vitamin D is effective in disease prevention? It does not. There are many differences between the two groups compared in addition to vitamin D consumption. People who take vitamin D regularly often take other steps to improve their health: exercise, diet, other vitamin supplements, choosing not to smoke. Any one of these factors could be influencing health. As described, this study does not necessarily prove that vitamin D is the key to disease prevention.

Experiments ultimately provide evidence to make decisions, so how could we narrow our focus and make claims of causality? In this section, you will learn important aspects of experimental design.

Designed Experiments

The purpose of an experiment is to investigate the relationship between two variables. When one variable causes change in another, we call the first variable the explanatory variable . The affected variable is called the response variable . In a randomized experiment, the researcher manipulates values of the explanatory variable and measures the resulting changes in the response variable. The different values of the explanatory variable may be called treatments . An experimental unit is a single object or individual to be measured. 

The main principles we want to follow in experimental design are:

Randomization

Replication.

In order to provide evidence that the explanatory variable is indeed causing the changes in the response variable, it is necessary to isolate the explanatory variable. The researcher must design their experiment in such a way that there is only one difference between groups being compared: the planned treatments. This is accomplished by randomization of experimental units to treatment groups. When subjects are assigned treatments randomly, all of the potential lurking variables are spread equally among the groups. At this point the only difference between groups is the one imposed by the researcher. Different outcomes measured in the response variable, therefore, must be a direct result of the different treatments. In this way, an experiment can show an apparent cause-and-effect connection between the explanatory and response variables.

Recall our previous example of investigating the effectiveness of vitamin D in preventing disease. Individuals in our trial could be randomly assigned, perhaps by flipping a coin, into one of two groups:  The control group (no treatment) and the second group receives extra doses of Vitamin D.

The more cases researchers observe, the more accurately they can estimate the effect of the explanatory variable on the response. In a single study, we replicate by collecting a sufficiently large sample. Additionally, a group of scientists may replicate an entire study to verify an earlier finding.  Having individuals experience a treatment more than once, called repeated measures is often helpful as well.

The power of suggestion can have an important influence on the outcome of an experiment. Studies have shown that the expectation of the study participant can be as important as the actual medication. In one study of performance-enhancing drugs, researchers noted:

Results showed that believing one had taken the substance resulted in [ performance ] times almost as fast as those associated with consuming the drug itself. In contrast, taking the drug without knowledge yielded no significant performance increment. [1]

It is often difficult to isolate the effects of the explanatory variable. To counter the power of suggestion, researchers set aside one treatment group as a control group . This group is given a placebo treatment–a treatment that cannot influence the response variable. The control group helps researchers balance the effects of being in an experiment with the effects of the active treatments. Of course, if you are participating in a study and you know that you are receiving a pill which contains no actual medication, then the power of suggestion is no longer a factor. Blinding in a randomized experiment preserves the power of suggestion. When a person involved in a research study is blinded, he does not know who is receiving the active treatment(s) and who is receiving the placebo treatment. A double-blind experiment is one in which both the subjects and the researchers involved with the subjects are blinded.

Randomized experiments are an essential tool in research. The US Food and Drug Administration typically requires that a new drug can only be marketed after two independently conducted randomized trials confirm its safety and efficacy; the European Medicines Agency has a similar policy. Large randomized experiments in medicine have provided the basis for major public health initiatives. In 1954 approximately 750,000 children participated in a randomized study comparing the polio vaccine with a placebo. In the United States, the results of the study quickly led to the widespread and successful use of the vaccine for polio prevention.

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

The Smell & Taste Treatment and Research Foundation conducted a study to investigate whether smell can affect learning. Subjects completed mazes multiple times while wearing masks. They completed the pencil and paper mazes three times wearing floral-scented masks, and three times with unscented masks. Participants were assigned at random to wear the floral mask during the first three trials or during the last three trials. For each trial, researchers recorded the time it took to complete the maze and the subject’s impression of the mask’s scent: positive, negative, or neutral.

More Experimental Design

There are many different experimental designs from the most basic, a single treatment and control group, to some very complicated designs.  In an experimental design setting, when working with more than one variable, or treatment, they are often called factors , especially if it is categorical .  The values of factors are are often called levels .  When there are multiple factors, the combinations of each of the levels are called treatment combinations , or interactions.  Some basic ones you may see are:

• Completely randomized
• Block design
• Matched pairs design

Completely Randomized

While very important and an essential research tool, not much explanation is needed for this design.  It involves figuring out how many treatments will be administered and randomly assigning participants to their respective groups.

Block Design 

Researchers sometimes know or suspect that variables, other than the treatment, influence the response. Under these circumstances, they may first group individuals based on this variable into blocks and then randomize cases within each block to the treatment groups. This strategy is often referred to as blocking. For instance, if we are looking at the effect of a drug on heart attacks, we might first split patients in the study into low-risk and high-risk blocks, then randomly assign half the patients from each block to the control group and the other half to the treatment group, as shown in the figure below. This strategy ensures each treatment group has an equal number of low-risk and high-risk patients.

Matched Pairs

A matched pairs design is one where we have very similar individuals (or even the same individual) receiving different two treatments (or treatment vs. control), then comparing their results.  This design is very powerful, however, it can be hard to find many like individuals to match up.  Some common ways of creating a matched pairs design are twin studies, before and after measurements,  pre and post test situations, or crossover studies.  Consider the following example:

In the 2000 Olympics, was the use of a new wetsuit design responsible for an observed increase in swim velocities? In a matched pairs study designed to investigate this question, twelve competitive swimmers swam 1500 meters at maximal speed, once wearing a wetsuit and once wearing a regular swimsuit. The order of wetsuit versus swimsuit was randomized for each of the 12 swimmers. Figure 1.6 shows the average velocity recorded for each swimmer, measured in meters per second (m/s).

Notice in this data, two sets of observations are uniquely paired so that an observation in one set matches an observation in the other; in this case, each swimmer has two measured velocities, one with a wetsuit and one with a swimsuit. A natural measure of the effect of the wetsuit on swim velocity is the difference between the measured maximum velocities (velocity.diff = wet.suit.velocity- swim.suit.velocity).  Even though there are two measurements per individual, using the difference in observations as the variable of interest allows for the problem to be analyzed.

A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without the new treatment. The same windshields are then treated, and the experiment is run again.  What experiment design is being implemented here?

A new medicine is said to help improve sleep. Eight subjects are picked at random and given the medicine. The means hours slept for each person were recorded before starting the medication and after. What experiment design is being implemented here?

Image References

Figure 1.5: Kindred Grey (2020). “Block Design.” CC BY-SA 4.0. Retrieved from https://commons.wikimedia.org/wiki/File:Block_Design.png

• McClung, M. Collins, D. “Because I know it will!”: placebo effects of an ergogenic aid on athletic performance. Journal of Sport & Exercise Psychology. 2007 Jun. 29(3):382-94. Web. April 30, 2013. ↵

Data collection where no variables are manipulated

Type of experiment where variables are manipulated; data is collected in a controlled setting

The independent variable in an experiment; the value controlled by researchers

The dependent variable in an experiment; the value that is measured for change at the end of an experiment

Different values or components of the explanatory variable applied in an experiment

Any individual or object to be measured

When an individual goes through a single treatment more than once

A group in a randomized experiment that receives no (or an inactive) treatment but is otherwise managed exactly as the other groups

An inactive treatment that has no real effect on the explanatory variable

Not telling participants which treatment they are receiving

The act of blinding both the subjects of an experiment and the researchers who work with the subjects

Variables in an experiment

Certain values of variables in an experiment

Combinations of levels of variables in an experiment

Dividing participants into treatment groups randomly

Grouping individuals based on a variable into "blocks" and then randomizing cases within each block to the treatment groups

Very similar individuals (or even the same individual) receive two different two treatments (or treatment vs. control) then the difference in results are compared

Significant Statistics Copyright © 2020 by John Morgan Russell, OpenStaxCollege, OpenIntro is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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AP Statistics : How to define experimental units

Study concepts, example questions & explanations for ap statistics, all ap statistics resources, example questions, example question #1 : how to conduct an experiment.

Of the following examples, which best describes quantitative data?

A child's gender.

Temperature measurements of water in degrees Fahrenheit.

A student's least favorite sport.

The softness of a chair.

College grade level-freshman, sophomore, junior, or senior.

Quantitative data describes a certain type of information that can be counted or expressed numerically and can be used in meaningful computations. Quantitative data is different from qualitative data, which is primarily involved in describing things in terms of categorizations or specific qualities. Looking at the answer choices, it is clear that measuring the temperature of water in degrees Fahrenheit is a numerical piece of information, and is thus quantitative.

When designing an experiment, what is the purpose of blocking?

To use chance to randomly assign experimental units to treatment groups (or vice versa)

To increase the number of experimental units

To hold an extraneous variable constant

None of the other answers

To separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments

The purpose of blocking, by definition, is to separate a particular sample into groups previously known to be similar in some way that are expected to affect response to treatments. The other choices pertain to control (keeping an extraneous variable constant), randomization (using random chance to assign experimental units to treatments), and replication (increasing the number of experimental units to reduce chance variation) in an experiment.

Example Question #2 : How To Conduct An Experiment

Which of the following is an example of qualitative data? 

The speed at which a car is traveling

The average SAT score of students at a particular high school 

The gender of a high school student

The temperature of a glass of water

The amount of carbon monoxide emissions in the air

The only example of qualitative data here is the gender of a high school student (i.e. male or female). This cannot be quantified, unlike the other answer choices which all have numbers, quantities, and amounts associated with them.

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• Animal characteristics
• Independent variables
• Group and sample size

Experimental unit

• Intervention
• Measurement
• Overview and demonstration of the EDA
• Getting the most out of the EDA
• What is the experiment diagram?
• Troubleshooting

How to identify the experimental unit in an in vivo experiment.

Why is the experimental unit important, the individual animal.

• A breeding female and litter
• The cage of animals

A part of an animal

An animal for a period of time, experiments with more than one experimental unit, representing the experimental unit in the eda.

The experimental unit is the entity you want to make inferences about (in the population) based on the sample (in your experiment).

The experimental unit is the entity subjected to an intervention independently of all other units. It must be possible to assign any two experimental units to different treatment groups. 

The sample size is the number of experimental units per group. You need enough experimental units in your experiment for reliable results. But, if you do not correctly identify the experimental unit, there is a risk you overestimate your sample size which could invalidate the results of your statistical analysis and conclusions.

The British Pharmacological Society have created an animated video to introduce the concept of experimental units and how correctly identifying them is important to interpret your results.

Back to top

Know your experimental unit

In animal experiments the experimental unit is often the individual animal. In this case, each animal is allocated to a particular treatment group independently of other animals. But this is not always the case. Depending on the treatment administered, the experimental unit may be bigger than the animal (e.g. a litter or a cage) or smaller than the animal (e.g. part of the animal or an animal for a period of time). You can learn more about how to identify your experimental unit using the examples in this section. 

Note that if you take multiple measurements from the same animal it does not mean that each animal provides multiple experimental units. The experimental unit is defined as the entity which receives an intervention or treatment, regardless of how many times you take measurements from it.

This is the most common situation and individual animals are independently assigned to distinct categories of the variable(s) of interest. It must be possible for any two individual animals to receive different treatments. 

An example could be an experiment with four groups defined by two variables of interest, sex and exercise. The categories of the variables of interest are 'female with exercise', 'female no exercise', 'male with exercise', and 'male no exercise'. Animals are either male or female independently of other animals, and each animal is allocated to different activity levels independently of the other animals. Thus, the experimental unit is the individual animal.  

A breeding female and litter 

Consider a teratogenesis experiment where the pregnant female receives a treatment and measurements are made on the individual pups after birth. Animals within a litter are all exposed to the same treatment – the experimental unit is therefore the whole litter. In this case, the variable  ‘individual pups’ is nested into the experimental unit ‘litter’.

The cage of animals 

If animals are group housed in a cage and all animals within that cage receive the same treatment, for example in the drinking water or diet, then the experimental unit is the cage of animals. 

However, if animals are group housed but can each receive a different treatment, for example by injection (and the treatment will not contaminate cage mates), then the experimental unit would be the individual animal.

If animals are exposed to a treatment via topical application, it may be possible to divide an area of skin into a number of different patches which can each receive distinct treatments. In this situation, the patch of skin on the animal is the experimental unit.

If individual cells can be stimulated independently and recording of the responses is made at the individual cell level, the experimental unit for the stimulation is the individual cell. Provided the experiment does not include another treatment which the whole animal is exposed to (e.g. drug injection or genotype), the individual cell can be the experimental unit for the whole experiment and a single animal provides many experimental units. It is important to note that if just a single animal is used, then the results hold true for that animal alone and cannot be generalised to the population.

When a single animal provides multiple experimental units, to avoid the confounding effect of between-animal variability, the individual animal should be used as a blocking factor and more than one animal should be used to improve generalisability. The number of animals needed depends on the between-animal variability.

Another scenario where a single animal can provide several experiment units is in a crossover experiment. In this experimental design, each animal is used as its own control and receives distinct treatments, separated by wash out periods. As animals can be exposed to different treatments in different test periods, the experimental unit is the animal for period of time.

Occasionally, there may be multiple experimental units in a single experiment, for example in a so-called split plot experiment.

Consider a situation where the effects of two different treatments (diet and vitamin supplements) on growth rate are investigated in mice. Diet is administered at the cage level and all mice housed in the same cage receive the same diet – the experimental unit for the diet treatment is therefore the cage. However, the vitamin supplement is administered by gavage meaning animals within the same cage can receive different supplements – the experimental unit for the vitamin supplement is the individual mouse.

This type of design is powerful as it enables researchers to investigate whether the effect of the vitamin is related to the diet administered. However the statistical analysis can be complicated and expert statistical advice should be sought before conducting such an experiment.

On your EDA diagram, the experimental unit is represented by the experimental unit node . This node is connected from one of the group nodes as shown in the image below.

If the experimental unit is the same throughout your experiment you only need one experimental unit node in your diagram. If there are multiple experimental units, multiple nodes may be necessary to clarify which unit different interventions are applied to.

Festing, MFW, et al. (2002). The design of animal experiments: reducing the use of animals in research through better experimental design . Royal Society of Medicine.

Lazic, SE (2010). The problem of pseudoreplication in neuroscientific studies: is it affecting your analysis? BMC Neurosci 11:5. doi: 10.1186/1471-2202-11-5

Lazic, SE, Clarke-Williams, CJ and Munafo, MR (2018). What exactly is 'N' in cell culture and animal experiments? PLOS Biol 16(4):e2005282. doi: 10.1371/journal.pbio.2005282

5.2 – Experimental units, Sampling units

Introduction, experimental units, experimental and sampling units often, but not always the same, replication: groups and individuals as sampling units, chapter 5 contents.

Sampling units  refer to the measured items, the focus of data collection; samples are selected from populations. Often, sampling units are the same thing as individuals. For example, if we are interested in the knowing whether men are more obese than women in Hawai’i, we would select individuals from the population; we would measure individuals. Thus, the sampling unit would be individuals, and the measurement unit would be percent body fat recorded for each individual. The data set would be the collection of all body fat measures for all individuals in the study, and we would then make inferences (draw conclusions) about the differences, if any, between adult males and females for body fat.

But sampling units can also refer to something more restrictive than the individual. For example, we may be interested in how stable, or consistent, is a person’s body fat over time. If we take a body fat measure once per year over a decade on the same group of adults, then the sampling unit refers to each observation of body fat recorded (once per year, ten times for an individual), and the population we are most likely to be referring to is the collection of all such readings (ten is arbitrary — we could have potentially measured the same individual thousands of times).

In some cases the researcher may wish to compare groups of individuals and not the individuals themselves. For example, a 2001 study sought to see if family structure influenced the metabolic (glycemic) control of children with diabetes (Thompson et al 2001). The researchers compared how well metabolic control was achieved in children of single parents and two-parent families. Thus, the sampling units would be families and not the individual children.

Experimental units  refers to the level at which treatments are independently applied in a study. Often, but not always, treatments are applied directly to individuals and therefore the sampling units and experimental units in these cases would be the same.

Question 1 : What is the sampling unit in the following cell experiment?

A technician thaws a cryo tube containing about ½ million A549 cells (Foster et al 1998) and grows the cells in a T-75 culture flask (the 75 corresponds to 75 cm 2  growing area) in a CO 2  incubator at 37 °C. After the cells reach about 70% confluency, which may represent hundreds of thousands of cells, the technician aliquots 1000 cells into twelve wells of a plate for a total of 12000 cells. To three wells the technician adds a cytokine, to another three wells he adds a cytokine inhibitor, and to another three wells he adds both the cytokine and it’s inhibitor, and to the last three wells he adds DMSO, which was the solvent for both the cytokine and the inhibitor. He then returns the plate to the incubator and 24 hours later extracts all of the cells and performs a multiplex quantitative PCR to determine gene expression of several target genes known to be relevant to cell proliferation.

The described experiment would be an example of a routine, but not trivial procedure the technician would do in the course of working on the project in a molecular biology laboratory.

The choices for numbers provided in the description we may consider for the number of sampling units are:

• 12,000 cells
• ½ million cells
• The target genes
• None of the above

The correct answer is G, None of the above.

“None of the above” because the correct answer is … there was just one sampling unit! All cells trace back to that single cryo tube.

To answer the question, start from the end and work your way back. What we are looking for is independence of samples and at what level in the experiment we find independence. Our basic choice is between numbers of cells and numbers of wells. Clearly, cells are contained in the wells, so all of the cells in one well share the same medium, being treated the same way, including all the way back to the cryo tube — all of the cells came from that one tube so this lack of independence traces all the way back to the source of the cells. Thus, the answer can’t be related to cell number. How many wells did the technician set up? Twelve total. So, the maximum number of sampling units would be twelve, unless the samples are not independent. And clearly the wells (samples) are not independent because, again, all cells in the twelve wells trace back to a single cryo tube. Thus, from both perspectives, wells and cells, the answer is actually just one sampling unit! (Cumming et al 2007; Lazic 2010). Finally, the genes themselves are the targets of our study — they are the variables, not the samples. Moreover, the same logic applies — all copies of the genes are in effect descended from the few cells used to start the population.

Question 2 : What is the experimental unit in the described cell experiment?

The correct answer is E, 12 wells. Noted above, the technician applied treatments to 12 wells. There were two treatments, cytokine and cytokine-inhibitor (Table 1).

Table 1. Translate experiment description to a table to better visualize the design

The correct identification of levels at which sampling independence occurs is crucial to successful interpretation of inferential statistics. Note replication in Table 1: three cytokine, three cytokine-inhibitor, three with both.  Sampling error rate is evaluated at the level of the sampling units. Technical replication of sampling units allows one to evaluate errors of measurement (e.g., instrument noise) (Blainey et al 2014). Replication of sampling units increases statistical power, the ability to correctly reject hypotheses. If the correct design reflects sampling units are groups and not individuals, then by counting the individuals as the independent sampling units would lead the researcher to think his design has more replication than it actually does. The consequence on the inferential statistics is that he will more likely reject a correct null hypothesis, in other words, the risk of elevated type I error occurs ( Chapter 8 – Inferential statistics ). This error, confusing individual and group sampling units, is called pseudoreplication  (Lazic 2010).

Consider a simpler experimental design scenario depicted in Figure 2: Three different water treatments (e.g., concentrations of synthetic progestins, Zeilinger et al. 2009) in bowls A, B, and C; three fish in bowl A, three fish in bowl B, and three fish in bowl C. The outcome variable might be a stress indicator, e.g., plasma cortisol (Luz et al 2008).

Figure 2. Three aquariums, three fish. Image modified from https://www.pngrepo.com/svg/153528/aquarium

Question 3 : What were the experimental units for the fish in the bowl experiment (Fig. 2)?

• Three bowls
• Three water treatments

The correct answer is A, 3 bowls. The treatments were allocated to the bowls, not to individual fish. The three fish in each bowl provides technical replication for the effects of bowl A, bowl B, and bowl C, but does not provide replication for the effects of the water treatments.  Adding three bowls for each water treatment, each with three fish, would be the simplest correction of the design, but may not be available to the researcher because of space or cost limitations. The design would then include nine bowls and 27 fish.  If resources are not available to simply scale up the design, then the researcher could repeat the study several times, taking care to control nuisance variables . Alternatively, if the treatments were applied to the individual fish, then the experimental units become the individual fish and the bowls reduced to a blocking effect ( Chapter 14.4 ), where differences may exist among the bowls, but they are no longer the level by which measurements are made. Note that if pseudoreplication is present in a study, this may be accounted for by specifying the error structure in a linear mixed model (e.g., random effects, blocking effects, etc., see Chapter 14 and Chapter 18 ).

Question 4 : What were the sampling units for the fish in the bowl experiment (Fig. 2)?

The correct answer is B, the individual fish. If instead of aqueous application of synthetic progestin, treatments were applied directly to each fish via injection, what would be the answers to Question 3 and Question 4?

Choices like these clearly involve additional compromises and assumptions about experimental design and inference about hypotheses.

Sampling units, experimental units, and the concept of level at which units are independent within an experiment were introduced. Lack of independence yields the problem of pseudoreplication in an experiment, which will increase the chance that we will detect differences between our treatment groups, when no such difference exists!

Figure 3. Three Miracle-Grow AeroGarden planters, each with nine seedlings of an Arabidopsis thaliana strain.

1. Nine seeds each of three strains of Arabidopsis thaliana were germinated in three Miracle-Grow AeroGarden ® hydroponic planters (Fig. 2). Each planter had nine or ten vials with sphagnum peat. All seeds from a strain were planted in the same apparatus, one seed per vial. What were the experimental units?

• strains of Arabidopsis
• vials in the planters

2. This experimental design is an example of pseudoreplication, but at what level?

3. How would you re-do this experiment to avoid pseudoreplication? (Hint: you can’t add more planters!)

• The basics explained
• Experiments
• Experimental and Sampling units
• Replication, Bias, and Nuisance Variables
• Clinical trials
• Importance of randomization in experimental design
• Sampling from Populations
• References and suggested readings

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1.4: Experimental Design and Ethics

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Does aspirin reduce the risk of heart attacks? Is one brand of fertilizer more effective at growing roses than another? Is fatigue as dangerous to a driver as the influence of alcohol? Questions like these are answered using randomized experiments. In this module, you will learn important aspects of experimental design. Proper study design ensures the production of reliable, accurate data.

The purpose of an experiment is to investigate the relationship between two variables. When one variable causes change in another, we call the first variable the explanatory variable . The affected variable is called the response variable. In a randomized experiment, the researcher manipulates values of the explanatory variable and measures the resulting changes in the response variable. The different values of the explanatory variable are called treatments . An experimental unit is a single object or individual to be measured.

You want to investigate the effectiveness of vitamin E in preventing disease. You recruit a group of subjects and ask them if they regularly take vitamin E. You notice that the subjects who take vitamin E exhibit better health on average than those who do not. Does this prove that vitamin E is effective in disease prevention? It does not. There are many differences between the two groups compared in addition to vitamin E consumption. People who take vitamin E regularly often take other steps to improve their health: exercise, diet, other vitamin supplements, choosing not to smoke. Any one of these factors could be influencing health. As described, this study does not prove that vitamin E is the key to disease prevention.

Additional variables that can cloud a study are called lurking variables . In order to prove that the explanatory variable is causing a change in the response variable, it is necessary to isolate the explanatory variable. The researcher must design her experiment in such a way that there is only one difference between groups being compared: the planned treatments. This is accomplished by the random assignment of experimental units to treatment groups. When subjects are assigned treatments randomly, all of the potential lurking variables are spread equally among the groups. At this point the only difference between groups is the one imposed by the researcher. Different outcomes measured in the response variable, therefore, must be a direct result of the different treatments. In this way, an experiment can prove a cause-and-effect connection between the explanatory and response variables.

The power of suggestion can have an important influence on the outcome of an experiment. Studies have shown that the expectation of the study participant can be as important as the actual medication. In one study of performance-enhancing drugs, researchers noted:

Results showed that believing one had taken the substance resulted in [ performance ] times almost as fast as those associated with consuming the drug itself. In contrast, taking the drug without knowledge yielded no significant performance increment. 1

When participation in a study prompts a physical response from a participant, it is difficult to isolate the effects of the explanatory variable. To counter the power of suggestion, researchers set aside one treatment group as a control group . This group is given a placebo treatment–a treatment that cannot influence the response variable. The control group helps researchers balance the effects of being in an experiment with the effects of the active treatments. Of course, if you are participating in a study and you know that you are receiving a pill which contains no actual medication, then the power of suggestion is no longer a factor. Blinding in a randomized experiment preserves the power of suggestion. When a person involved in a research study is blinded, he does not know who is receiving the active treatment(s) and who is receiving the placebo treatment. A double-blind experiment is one in which both the subjects and the researchers involved with the subjects are blinded.

Example \(\PageIndex{1}\)

Researchers want to investigate whether taking aspirin regularly reduces the risk of heart attack. Four hundred men between the ages of 50 and 84 are recruited as participants. The men are divided randomly into two groups: one group will take aspirin, and the other group will take a placebo. Each man takes one pill each day for three years, but he does not know whether he is taking aspirin or the placebo. At the end of the study, researchers count the number of men in each group who have had heart attacks.

Identify the following values for this study: population, sample, experimental units, explanatory variable, response variable, treatments.

• The population is men aged 50 to 84.
• The sample is the 400 men who participated.
• The experimental units are the individual men in the study.
• The explanatory variable is oral medication.
• The treatments are aspirin and a placebo.
• The response variable is whether a subject had a heart attack.

Example \(\PageIndex{2}\)

The Smell & Taste Treatment and Research Foundation conducted a study to investigate whether smell can affect learning. Subjects completed mazes multiple times while wearing masks. They completed the pencil and paper mazes three times wearing floral-scented masks, and three times with unscented masks. Participants were assigned at random to wear the floral mask during the first three trials or during the last three trials. For each trial, researchers recorded the time it took to complete the maze and the subject’s impression of the mask’s scent: positive, negative, or neutral.

• Describe the explanatory and response variables in this study.
• What are the treatments?
• Identify any lurking variables that could interfere with this study.
• Is it possible to use blinding in this study?
• The explanatory variable is scent, and the response variable is the time it takes to complete the maze.
• There are two treatments: a floral-scented mask and an unscented mask.
• All subjects experienced both treatments. The order of treatments was randomly assigned so there were no differences between the treatment groups. Random assignment eliminates the problem of lurking variables.
• Subjects will clearly know whether they can smell flowers or not, so subjects cannot be blinded in this study. Researchers timing the mazes can be blinded, though. The researcher who is observing a subject will not know which mask is being worn.

Example \(\PageIndex{3}\)

A researcher wants to study the effects of birth order on personality. Explain why this study could not be conducted as a randomized experiment. What is the main problem in a study that cannot be designed as a randomized experiment?

The explanatory variable is birth order. You cannot randomly assign a person’s birth order. Random assignment eliminates the impact of lurking variables. When you cannot assign subjects to treatment groups at random, there will be differences between the groups other than the explanatory variable.

Exercise \(\PageIndex{4}\)

You are concerned about the effects of texting on driving performance. Design a study to test the response time of drivers while texting and while driving only. How many seconds does it take for a driver to respond when a leading car hits the brakes?

• Describe the explanatory and response variables in the study.
• What should you consider when selecting participants?
• Your research partner wants to divide participants randomly into two groups: one to drive without distraction and one to text and drive simultaneously. Is this a good idea? Why or why not?
• How can blinding be used in this study?
• Explanatory: presence of distraction from texting; response: response time measured in seconds
• Driving without distraction and driving while texting
• Answers will vary. Possible responses: Do participants regularly send and receive text messages? How long has the subject been driving? What is the age of the participants? Do participants have similar texting and driving experience?
• This is not a good plan because it compares drivers with different abilities. It would be better to assign both treatments to each participant in random order.
• Possible responses include: texting ability, driving experience, type of phone.
• The researchers observing the trials and recording response time could be blinded to the treatment being applied.

The widespread misuse and misrepresentation of statistical information often gives the field a bad name. Some say that “numbers don’t lie,” but the people who use numbers to support their claims often do.

A recent investigation of famous social psychologist, Diederik Stapel, has led to the retraction of his articles from some of the world’s top journals including Journal of Experimental Social Psychology, Social Psychology, Basic and Applied Social Psychology, British Journal of Social Psychology, and the magazine Science . Diederik Stapel is a former professor at Tilburg University in the Netherlands. Over the past two years, an extensive investigation involving three universities where Stapel has worked concluded that the psychologist is guilty of fraud on a colossal scale. Falsified data taints over 55 papers he authored and 10 Ph.D. dissertations that he supervised.

Stapel did not deny that his deceit was driven by ambition. But it was more complicated than that, he told me. He insisted that he loved social psychology but had been frustrated by the messiness of experimental data, which rarely led to clear conclusions. His lifelong obsession with elegance and order, he said, led him to concoct sexy results that journals found attractive. “It was a quest for aesthetics, for beauty—instead of the truth,” he said. He described his behavior as an addiction that drove him to carry out acts of increasingly daring fraud, like a junkie seeking a bigger and better high. 2

The committee investigating Stapel concluded that he is guilty of several practices including:

• creating datasets, which largely confirmed the prior expectations,
• altering data in existing datasets,
• changing measuring instruments without reporting the change, and
• misrepresenting the number of experimental subjects.

Clearly, it is never acceptable to falsify data the way this researcher did. Sometimes, however, violations of ethics are not as easy to spot.

Researchers have a responsibility to verify that proper methods are being followed. The report describing the investigation of Stapel’s fraud states that, “statistical flaws frequently revealed a lack of familiarity with elementary statistics.” 3 Many of Stapel’s co-authors should have spotted irregularities in his data. Unfortunately, they did not know very much about statistical analysis, and they simply trusted that he was collecting and reporting data properly.

Many types of statistical fraud are difficult to spot. Some researchers simply stop collecting data once they have just enough to prove what they had hoped to prove. They don’t want to take the chance that a more extensive study would complicate their lives by producing data contradicting their hypothesis.

Professional organizations, like the American Statistical Association, clearly define expectations for researchers. There are even laws in the federal code about the use of research data.

When a statistical study uses human participants, as in medical studies, both ethics and the law dictate that researchers should be mindful of the safety of their research subjects. The U.S. Department of Health and Human Services oversees federal regulations of research studies with the aim of protecting participants. When a university or other research institution engages in research, it must ensure the safety of all human subjects. For this reason, research institutions establish oversight committees known as Institutional Review Boards (IRB) . All planned studies must be approved in advance by the IRB. Key protections that are mandated by law include the following:

• Risks to participants must be minimized and reasonable with respect to projected benefits.
• Participants must give informed consent . This means that the risks of participation must be clearly explained to the subjects of the study. Subjects must consent in writing, and researchers are required to keep documentation of their consent.
• Data collected from individuals must be guarded carefully to protect their privacy.

These ideas may seem fundamental, but they can be very difficult to verify in practice. Is removing a participant’s name from the data record sufficient to protect privacy? Perhaps the person’s identity could be discovered from the data that remains. What happens if the study does not proceed as planned and risks arise that were not anticipated? When is informed consent really necessary? Suppose your doctor wants a blood sample to check your cholesterol level. Once the sample has been tested, you expect the lab to dispose of the remaining blood. At that point the blood becomes biological waste. Does a researcher have the right to take it for use in a study?

It is important that students of statistics take time to consider the ethical questions that arise in statistical studies. How prevalent is fraud in statistical studies? You might be surprised—and disappointed. There is a website (www.retractionwatch.com) dedicated to cataloging retractions of study articles that have been proven fraudulent. A quick glance will show that the misuse of statistics is a bigger problem than most people realize.

Vigilance against fraud requires knowledge. Learning the basic theory of statistics will empower you to analyze statistical studies critically.

Example \(\PageIndex{5}\)

Describe the unethical behavior in each example and describe how it could impact the reliability of the resulting data. Explain how the problem should be corrected.

A researcher is collecting data in a community.

• She selects a block where she is comfortable walking because she knows many of the people living on the street.
• No one seems to be home at four houses on her route. She does not record the addresses and does not return at a later time to try to find residents at home.
• She skips four houses on her route because she is running late for an appointment. When she gets home, she fills in the forms by selecting random answers from other residents in the neighborhood.
• By selecting a convenient sample, the researcher is intentionally selecting a sample that could be biased. Claiming that this sample represents the community is misleading. The researcher needs to select areas in the community at random.
• Intentionally omitting relevant data will create bias in the sample. Suppose the researcher is gathering information about jobs and child care. By ignoring people who are not home, she may be missing data from working families that are relevant to her study. She needs to make every effort to interview all members of the target sample.
• It is never acceptable to fake data. Even though the responses she uses are “real” responses provided by other participants, the duplication is fraudulent and can create bias in the data. She needs to work diligently to interview everyone on her route.

Exercise \(\PageIndex{6}\)

Describe the unethical behavior, if any, in each example and describe how it could impact the reliability of the resulting data. Explain how the problem should be corrected.

A study is commissioned to determine the favorite brand of fruit juice among teens in California.

• The survey is commissioned by the seller of a popular brand of apple juice.
• There are only two types of juice included in the study: apple juice and cranberry juice.
• Researchers allow participants to see the brand of juice as samples are poured for a taste test.
• Twenty-five percent of participants prefer Brand X, 33% prefer Brand Y and 42% have no preference between the two brands. Brand X references the study in a commercial saying “Most teens like Brand X as much as or more than Brand Y.”
• This is not necessarily a problem. The study should be monitored carefully, however, to ensure that the company is not pressuring researchers to return biased results.
• If the researchers truly want to determine the favorite brand of juice, then researchers should ask teens to compare different brands of the same type of juice. Choosing a sweet juice to compare against a sharp-flavored juice will not lead to an accurate comparison of brand quality.
• Participants could be biased by the knowledge. The results may be different from those obtained in a blind taste test.
• The commercial tells the truth, but not the whole truth. It leads consumers to believe that Brand X was preferred by more participants than Brand Y while the opposite is true.
• “Vitamin E and Health,” Nutrition Source, Harvard School of Public Health, www.hsph.harvard.edu/nutritio...rce/vitamin-e/ (accessed May 1, 2013).
• Stan Reents. “Don’t Underestimate the Power of Suggestion,” athleteinme.com, http://www.athleteinme.com/ArticleView.aspx?id=1053 (accessed May 1, 2013).
• Ankita Mehta. “Daily Dose of Aspiring Helps Reduce Heart Attacks: Study,” International Business Times, July 21, 2011. Also available online at http://www.ibtimes.com/daily-dose-as...s-study-300443 (accessed May 1, 2013).
• The Data and Story Library, lib.stat.cmu.edu/DASL/Stories...dLearning.html (accessed May 1, 2013).
• M.L. Jacskon et al., “Cognitive Components of Simulated Driving Performance: Sleep Loss effect and Predictors,” Accident Analysis and Prevention Journal, Jan no. 50 (2013), http://www.ncbi.nlm.nih.gov/pubmed/22721550 (accessed May 1, 2013).
• “Earthquake Information by Year,” U.S. Geological Survey. earthquake.usgs.gov/earthquak...archives/year/ (accessed May 1, 2013).
• “Fatality Analysis Report Systems (FARS) Encyclopedia,” National Highway Traffic and Safety Administration. http://www-fars.nhtsa.dot.gov/Main/index.aspx (accessed May 1, 2013).
• Data from www.businessweek.com (accessed May 1, 2013).
• Data from www.forbes.com (accessed May 1, 2013).
• “America’s Best Small Companies,” http://www.forbes.com/best-small-companies/list/ (accessed May 1, 2013).
• U.S. Department of Health and Human Services, Code of Federal Regulations Title 45 Public Welfare Department of Health and Human Services Part 46 Protection of Human Subjects revised January 15, 2009. Section 46.111:Criteria for IRB Approval of Research.
• “April 2013 Air Travel Consumer Report,” U.S. Department of Transportation, April 11 (2013), www.dot.gov/airconsumer/april...onsumer-report (accessed May 1, 2013).
• Lori Alden, “Statistics can be Misleading,” econoclass.com, http://www.econoclass.com/misleadingstats.html (accessed May 1, 2013).
• Maria de los A. Medina, “Ethics in Statistics,” Based on “Building an Ethics Module for Business, Science, and Engineering Students” by Jose A. Cruz-Cruz and William Frey, Connexions, http://cnx.org/content/m15555/latest/ (accessed May 1, 2013).

A poorly designed study will not produce reliable data. There are certain key components that must be included in every experiment. To eliminate lurking variables, subjects must be assigned randomly to different treatment groups. One of the groups must act as a control group, demonstrating what happens when the active treatment is not applied. Participants in the control group receive a placebo treatment that looks exactly like the active treatments but cannot influence the response variable. To preserve the integrity of the placebo, both researchers and subjects may be blinded. When a study is designed properly, the only difference between treatment groups is the one imposed by the researcher. Therefore, when groups respond differently to different treatments, the difference must be due to the influence of the explanatory variable.

“An ethics problem arises when you are considering an action that benefits you or some cause you support, hurts or reduces benefits to others, and violates some rule.” 4 Ethical violations in statistics are not always easy to spot. Professional associations and federal agencies post guidelines for proper conduct. It is important that you learn basic statistical procedures so that you can recognize proper data analysis.

Exercise \(\PageIndex{7}\)

Design an experiment. Identify the explanatory and response variables. Describe the population being studied and the experimental units. Explain the treatments that will be used and how they will be assigned to the experimental units. Describe how blinding and placebos may be used to counter the power of suggestion.

Discuss potential violations of the rule requiring informed consent.

• Inmates in a correctional facility are offered good behavior credit in return for participation in a study.
• A research study is designed to investigate a new children’s allergy medication.
• Participants in a study are told that the new medication being tested is highly promising, but they are not told that only a small portion of participants will receive the new medication. Others will receive placebo treatments and traditional treatments.
• Inmates may not feel comfortable refusing participation, or may feel obligated to take advantage of the promised benefits. They may not feel truly free to refuse participation.
• Parents can provide consent on behalf of their children, but children are not competent to provide consent for themselves.
• All risks and benefits must be clearly outlined. Study participants must be informed of relevant aspects of the study in order to give appropriate consent.

1 McClung, M. Collins, D. “Because I know it will!”: placebo effects of an ergogenic aid on athletic performance. Journal of Sport & Exercise Psychology. 2007 Jun. 29(3):382-94. Web. April 30, 2013.

2 Y.udhijit Bhattacharjee, “The Mind of a Con Man,” Magazine, New York Times, April 26, 2013. Available online at: http://www.nytimes.com/2013/04/28/ma...src=dayp&_r=2& (accessed May 1, 2013).

3 “Flawed Science: The Fraudulent Research Practices of Social Psychologist Diederik Stapel,” Tillburg University, November 28, 2012, www.tilburguniversity.edu/upl...012_UK_web.pdf (accessed May 1, 2013).

4 Andrew Gelman, “Open Data and Open Methods,” Ethics and Statistics, http://www.stat.columbia.edu/~gelman...nceEthics1.pdf (accessed May 1, 2013).

• Why Study Statistics?
• Descriptive & Inferential Statistics

Fundamental Elements of Statistics

• Quantitative and Qualitative Data
• Measurement Data Levels
• Collecting Data
• Ethics in Statistics
• Describing Qualitative Data
• Describing Quantitative Data
• Stem-and-Leaf Plots
• Measures of Central Tendency
• Measures of Variability
• Describing Data using the Mean and Standard Deviation
• Measures of Position
• Counting Techniques
• Simple & Compound Events
• Independent and Dependent Events
• Mutually Exclusive and Non-Mutually Exclusive Events
• Permutations and Combinations
• Normal Distribution
• Central Limit Theorem
• Confidence Intervals
• Determining the Sample Size
• Hypothesis Testing
• Hypothesis Testing Process

Statistical methods are particularly useful for studying, analyzing, and learning about populations of experimental units.

Examples of populations: 

• All students at Centennial
• Everybody in Ontario
• Every flight leaving Pearson Airport
• Every grain of sand on a beach.

Examples of variables:

• The student number, program of study, and year of study of Centennial students
• The age, current occupation, and number of people in current household of someone in Ontario 
• The departure time and destination of flights leaving Pearson.
• The size and weight of each grain of sand on a beach.

It is nearly impossible to measure each grain of sand on a bench, so instead of collecting the population, we can estimate using a sample.

Examples of statistical inferences:

• Using the average age of a student of one class to estimate the average age of Centennial students.
• The tallest or shortest person of the first 100 people you encounter to estimate the tallest or shortest in Ontario.

However, the accuracy of the statistical inference depends on how reliable it is.

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• Next: Quantitative and Qualitative Data >>
• Last Updated: Apr 20, 2023 12:47 PM
• URL: https://libraryguides.centennialcollege.ca/c.php?g=717168

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Identifying the experimental unit

I have included a diagram of an experiment where cells are pooled from multiple animals, cells from the pool are then allocated to different treatments and a measurement is taken from each individual cell in each treatment. The aim of this experiment is to determine how doses of a drug (treatments) affect cell size. I have previously received different opinions on what constitutes the experimental unit in this case. I would say the experimental unit is the pool so n=1 but when looking at the definition of experimental unit it states: “The smallest division of the experimental material such that any two experimental units can receive different treatments” - surely two individual cells could theoretically receive different treatments since they are separate entities?

Most examples I have found are more straight forward, for example had the snails themselves been exposed to the treatment I could see how the cells within each snail would no longer be independent and thus the snail would be the experimental unit.

• experiment-design
• biostatistics

• $\begingroup$ Welcome to CrossValidated. I think the EUs are the pools, because it is those that are assigned to treatments. I think you must be using the word "treatment" in a different sense in the last sentence of your 1st paragraph. It is what is assigned to treatments that matters. $\endgroup$ –  Russ Lenth Commented Aug 20, 2014 at 15:16
• $\begingroup$ About how many individual cells are subjected to each of the 6 treatments? $\endgroup$ –  half-pass Commented Aug 20, 2014 at 19:00
• $\begingroup$ Why are you grouping the cells from different individuals? Isn't it possible that the cells from different animals react differently to each treatment? $\endgroup$ –  Rodrigo Commented Aug 20, 2014 at 19:31
• $\begingroup$ Hi, the cells from different individuals are pooled because a single snail doesn't produce a large enough volume to use $\endgroup$ –  John Smith Commented Aug 21, 2014 at 10:05

Since you're assigning individual cells to treatments and measuring sizes of individual cells, the experimental unit is individual cells .

You're not keeping track of which snail contributed each cell, so the number of snails is only relevant to generalizability, not sample size. In other words, although you may have a very large sample of cells, they are coming from a small population. If you knew which snail contributed each cell, you could account for inter-snail variability by treating each snail as a cluster from which you draw individual units (cells). But when it comes to cell size, this would probably not accomplish much anyway.

• $\begingroup$ Thanks, I've gone back and forth between the pool and the cell. I suppose it depends on the question being asked i.e are we looking at difference between snails or between cells and in my case I'm interested in difference between cells. $\endgroup$ –  John Smith Commented Aug 21, 2014 at 10:07
• 1 $\begingroup$ I disagree. To me the UE is each well receiving a treatment and the cells are sample units. The pool receive the same treatment. $\endgroup$ –  Emilie Commented Aug 21, 2014 at 12:26
• 1 $\begingroup$ I found this quote: "There is controversy amongst statisticians and biologists as to the most appropriate experimental unit when, for example, several animals are fed together within a pen or paddock. Broadly speaking, these positions can be divided into a view that the most appropriate experimental unit is the smallest unit upon which a treatment can be applied (generally the group of animals) versus a view that the most appropriate experimental unit is the smallest unit upon which a measurement can be made (generally the animal)." $\endgroup$ –  John Smith Commented Aug 21, 2014 at 13:08
• 1 $\begingroup$ Perhaps the seminal paper of Hulbert would help you : Hurlbert, S. H. 1984. Pseudoreplication and the design of ecological field experiments. — Ecol. Monogr. 54: 187-211. As it's made for ecologist, it will probably be better than statisticians definitions. But in your case, all the cell in your treatment "wells" receive the same treatment. It seems quite clear they are sample units. $\endgroup$ –  Emilie Commented Aug 21, 2014 at 19:08
• 2 $\begingroup$ Ah, I didn't realize there were multiple wells for each dose. In that case, I would consider this a cluster design that could be analyzed with, e.g., a multilevel model. The clusters are the wells and the individuals within each cluster are the cells. $\endgroup$ –  half-pass Commented Aug 21, 2014 at 19:41

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Observation in Statistics: Simple Definition & Examples

Statistics Definitions >

What is an Observation in Statistics?

General Meaning of Observation in Statistics

An observation in statistics is a value of something of interest you’re measuring or counting during a study or experiment: a person’s height, a bank account value at a certain point in time, or number of animals. “Observation unit” means the same thing in this context. For example, let’s say you are measuring how well your savings perform over the period of one year. You record one measurement (your bank account balance) every three months for a total of four observations :

• March = $564
• June = $576
• September = $587
• December = $599

Note that an “observation” doesn’t imply that you observed it. Somebody else might have measured it. Or it could be data you found in a dusty file and have no idea where it came from. Lets say you found one thousand files. Each file could be an observation, or each page within the file; a lot depends on you , and how you choose to break apart your data. Basically, a lot depends on what you’re looking for. Let’s say your files contain data from an 1800’s asylum, and you’re interested in the health of women in the asylum. The file covers would be of no use to you, so they obviously would not be “observations”, but what about the rest of the contents? You might choose to take each person’s file and classify that as an experimental unit. However, if you’re only interested in the rate of, say, syphilis, then you might only take each syphilis case.

Notation for experimental units

An observation in statistics usually denoted by the letter X. Each of these observational units (X) represents data from a single observation.

In Research

Empirical research is where you conduct “hands on” experimentation. In other words, you get your results from actual experience rather than from a theory or belief. In this context, “observation” is what you do —you observe things happening. For example, an Observational Study is where the researcher observes participants without any kind of interference.

Observation can also, in a very narrow sense, apply to the actual observer . For example, observation bias happens when key information is either collected, interpreted or measured inaccurately. According to Johns Hopkins , it’s when:

“…information is collected differently between two groups, leading to an error in the conclusion of the association.”

This broad category contains Observer Bias , which happens when a researcher is aware of a disease or exposure status.

Kanchanaraksa, S. (2008). Bias and Confounding. Johns Hopkins Bloomberg School of Public Health. Retrieved June 7, 2018 from: http://ocw.jhsph.edu/courses/fundepiii/pdfs/lecture18.pdf