example of experimental study in statistics

Observational vs Experimental Study

Is your statistical study observational or experimental let us find out..

Chetna Khanna

Towards Data Science

Statistics is the science and the art of learning from data. 🎓 As a discipline, it is not only concerned with the collection, analysis, and interpretation of data but also with the presentation and communication of results based on the analysis performed on the data.

The purpose of a study is often to investigate the relationship between two or more variables involved in the study. For example, does exercise reduce weight? or do people who drink milk before bedtime tend to go to sleep earlier than the people who drink coffee?

The study we conduct to perform statistical analysis of our data can majorly be of two types — Observational and Experimental.

When we read about any research, we usually do not pay attention to how the study was designed. However, to understand the quality of the results/findings claimed by the study, it is extremely important for us to know this.

I myself never paid attention to any research as to how it has been designed and rather believed the claims made by it. I know that was a stupid move but yes I was unaware of the types of studies earlier. I hope you guys are aware of them. If not, then this article can help you understand the concept well. 😎

A simple example of research that many people generally believe to be accurate is regarding food/health/nutrition. They are generally in the news headlines and widely shared on social media too. One day we might read a study claiming that eggs increase the risk of cancer and the following day we might read a claim saying that they are extremely healthy. (Note that, this is just an example to state my point clearly).

We can observe that different studies claim most food items to be either positively or negatively associated with health, which might be true in some sense. For example, the excess intake of a highly nutritious food item can negatively affect the body. But it is extremely important to make sure that the evidence/claim we are reading about is reliable or not.

So, let us find out what these studies tell us using some example problems.

1. Observational Study 👀

In this type of study, we measure or survey members of a sample without trying to affect the members or manipulating the variables. Here, we simply observe what is happening and record the observations. So, it would be correct to say that researchers do not impose any kind of treatment or restriction to the group nor do they randomly assign the subjects to a group. There is basically no manipulation of the environment in which the subject occurs.

Thus, this type of study shows that there may be a relationship between variables but it is not necessary to be a cause and effect (causal) relationship. And, even if the observational study shows a cause-effect relationship, the evidence provided by it is generally considered to be weak.

An opinion survey asking questions about how people liked the most recent documentary is an example of an observational study. Here, the researchers have no control over the participants.

Some of the key points about observational studies are as follows:

• Observational studies are less expensive than experimental studies.
• The time required for the completion of observational studies can be several years to decades.

2. Experimental Study 💊

In this type of study, we randomly assign a treatment to a group so that the researchers can draw the cause and effect (causal) conclusion. This random assignment of treatments is what distinguishes both the studies (observational and experimental). Here, we experiment and manipulate the environment of the subject to measure the response (dependent) variable. Evidence provided by the experimental study is considered to be stronger than the observational study.

This type of study is also sometimes called a scientific study because of the treatment involved in it.

Note: The experimental study involves two groups — experiment group and control group. Control group is the group in the study that does not receive treatment by the researchers.

Some of the key points about experimental studies are as follows:

• Experimental studies are closely monitored.
• Experimental studies are expensive.
• Experimental studies are typically smaller and shorter than observational studies.

Now, let us understand the difference between the two types of studies using different problems.

A study took a random sample of students and asked them about their bedtime schedules. The data showed that people who sleep for at least 8 hours before the exam day were more likely to get good grades than those who sleep for less than 8 hours.

Type of Study: Observational

Reason: The study is a kind of a survey that just asked people about the number of hours they sleep right before the exam day and how many marks they scored. Since the people were not randomly assigned to any group or given any treatment, the study was an observational study.

A study randomly assigned people to one of the two groups. Group 1 was asked to follow a strict study schedule for a fixed period of time whereas Group 2 was asked to study in the same way as they used to earlier. The researchers looked at which group scored better in the exams.

Type of Study: Experimental

Reason: The study randomly assigned people to two different groups out of which one group was given a treatment whereas the other group was not. Thus, this was an experimental study.

A study took a random sample of people and examined their smoking habits. Each person was classified as either a light, moderate or heavy smoker. The researcher looked at the stress level of each group.

Reason: The study took a random sample of people but does not randomly assign people to different groups. The study simply observed whether the people were light, moderate, or heavy smokers and their stress level. Thus, this was an observational study.

I hope you can now distinguish between experimental and observational studies and can even take responsible decisions for yourself after reading any study.

Do check out my other articles on Towards Data Science .

Happy reading! 📗 🖌

Written by Chetna Khanna

Engineer — Data & ML | Love to read | Love to write I https://www.linkedin.com/in/chetna-khanna/

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Calcworkshop

Experimental Design in Statistics w/ 11 Examples!

// Last Updated: September 20, 2020 - Watch Video //

A proper experimental design is a critical skill in statistics.

Jenn, Founder Calcworkshop ® , 15+ Years Experience (Licensed & Certified Teacher)

Without proper controls and safeguards, unintended consequences can ruin our study and lead to wrong conclusions.

So let’s dive in to see what’s this is all about!

What’s the difference between an observational study and an experimental study?

An observational study is one in which investigators merely measure variables of interest without influencing the subjects.

And an experiment is a study in which investigators administer some form of treatment on one or more groups?

In other words, an observation is hands-off, whereas an experiment is hands-on.

So what’s the purpose of an experiment?

To establish causation (i.e., cause and effect).

All this means is that we wish to determine the effect an independent explanatory variable has on a dependent response variable.

The explanatory variable explains a response, similar to a child falling and skins their knee and starting to cry. The child is crying in response to falling and skinning their knee. So the explanatory variable is the fall, and the response variable is crying.

Explanatory Vs Response Variable In Everyday Life

Let’s look at another example. Suppose a medical journal describes two studies in which subjects who had a seizure were randomly assigned to two different treatments:

• No treatment.
• A high dose of vitamin C.

The subjects were observed for a year, and the number of seizures for each subject was recorded. Identify the explanatory variable (independent variable), response variable (dependent variable), and include the experimental units.

The explanatory variable is whether the subject received either no treatment or a high dose of vitamin C. The response variable is whether the subject had a seizure during the time of the study. The experimental units in this study are the subjects who recently had a seizure.

Okay, so using the example above, notice that one of the groups did not receive treatment. This group is called a control group and acts as a baseline to see how a new treatment differs from those who don’t receive treatment. Typically, the control group is given something called a placebo, a substance designed to resemble medicine but does not contain an active drug component. A placebo is a dummy treatment, and should not have a physical effect on a person.

Before we talk about the characteristics of a well-designed experiment, we need to discuss some things to look out for:

• Confounding
• Lurking variables

Confounding happens when two explanatory variables are both associated with a response variable and also associated with each other, causing the investigator not to be able to identify their effects and the response variable separately.

A lurking variable is usually unobserved at the time of the study, which influences the association between the two variables of interest. In essence, a lurking variable is a third variable that is not measured in the study but may change the response variable.

For example, a study reported a relationship between smoking and health. A study of 1430 women were asked whether they smoked. Ten years later, a follow-up survey observed whether each woman was still alive or deceased. The researchers studied the possible link between whether a woman smoked and whether she survived the 10-year study period. They reported that:

• 21% of the smokers died
• 32% of the nonsmokers died

So, is smoking beneficial to your health, or is there something that could explain how this happened?

Older women are less likely to be smokers, and older women are more likely to die. Because age is a variable that influences the explanatory and response variable, it is considered a confounding variable.

But does smoking cause death?

Notice that the lurking variable, age, can also be a contributing factor. While there is a correlation between smoking and mortality, and also a correlation between smoking and age, we aren’t 100% sure that they are the cause of the mortality rate in women.

Lurking – Confounding – Correlation – Causation Diagram

Now, something important to point out is that a lurking variable is one that is not measured in the study that could influence the results. Using the example above, some other possible lurking variables are:

• Stress Level.

These variables were not measured in the study but could influence smoking habits as well as mortality rates.

What is important to note about the difference between confounding and lurking variables is that a confounding variable is measured in a study, while a lurking variable is not.

Additionally, correlation does not imply causation!

Alright, so now it’s time to talk about blinding: single-blind, double-blind experiments, as well as the placebo effect.

A single-blind experiment is when the subjects are unaware of which treatment they are receiving, but the investigator measuring the responses knows what treatments are going to which subject. In other words, the researcher knows which individual gets the placebo and which ones receive the experimental treatment. One major pitfall for this type of design is that the researcher may consciously or unconsciously influence the subject since they know who is receiving treatment and who isn’t.

A double-blind experiment is when both the subjects and investigator do not know who receives the placebo and who receives the treatment. A double-blind model is considered the best model for clinical trials as it eliminates the possibility of bias on the part of the researcher and the possibility of producing a placebo effect from the subject.

The placebo effect is when a subject has an effect or response to a fake treatment because they “believe” that the result should occur as noted by Yale . For example, a person struggling with insomnia takes a placebo (sugar pill) but instantly falls asleep because they believe they are receiving a sleep aid like Ambien or Lunesta.

Placebo Effect – Real Life Example

So, what are the three primary requirements for a well-designed experiment?

• Randomization

In a controlled experiment , the researchers, or investigators, decide which subjects are assigned to a control group and which subjects are assigned to a treatment group. In doing so, we ensure that the control and treatment groups are as similar as possible, and limit possible confounding influences such as lurking variables. A replicated experiment that is repeated on many different subjects helps reduce the chance of variation on the results. And randomization means we randomly assign subjects into control and treatment groups.

When subjects are divided into control groups and treatment groups randomly, we can use probability to predict the differences we expect to observe. If the differences between the two groups are higher than what we would expect to see naturally (by chance), we say that the results are statistically significant.

For example, if it is surmised that a new medicine reduces the effects of illness from 72 hours to 71 hours, this would not be considered statistically significant. The difference from 72 hours to 71 hours is not substantial enough to support that the observed effect was due to something other than normal random variation.

Now there are two major types of designs:

• Completely-Randomized Design (CRD)
• Block Design

A completely randomized design is the process of assigning subjects to control and treatment groups using probability, as seen in the flow diagram below.

Completely Randomized Design Example

A block design is a research method that places subjects into groups of similar experimental units or conditions, like age or gender, and then assign subjects to control and treatment groups using probability, as shown below.

Randomized Block Design Example

Additionally, a useful and particular case of a blocking strategy is something called a matched-pair design . This is when two variables are paired to control for lurking variables.

For example, imagine we want to study if walking daily improved blood pressure. If the blood pressure for five subjects is measured at the beginning of the study and then again after participating in a walking program for one month, then the observations would be considered dependent samples because the same five subjects are used in the before and after observations; thus, a matched-pair design.

Please note that our video lesson will not focus on quasi-experiments. A quasi experimental design lacks random assignments; therefore, the independent variable can be manipulated prior to measuring the dependent variable, which may lead to confounding. For the sake of our lesson, and all future lessons, we will be using research methods where random sampling and experimental designs are used.

Together we will learn how to identify explanatory variables (independent variable) and response variables (dependent variables), understand and define confounding and lurking variables, see the effects of single-blind and double-blind experiments, and design randomized and block experiments.

Experimental Designs – Lesson & Examples (Video)

1 hr 06 min

• Introduction to Video: Experiments
• 00:00:29 – Observational Study vs Experimental Study and Response and Explanatory Variables (Examples #1-4)
• Exclusive Content for Members Only
• 00:09:15 – Identify the response and explanatory variables and the experimental units and treatment (Examples #5-6)
• 00:14:47 – Introduction of lurking variables and confounding with ice cream and homicide example
• 00:18:57 – Lurking variables, Confounding, Placebo Effect, Single Blind and Double Blind Experiments (Example #7)
• 00:27:20 – What was the placebo effect and was the experiment single or double blind? (Example #8)
• 00:30:36 – Characteristics of a well designed and constructed experiment that is statistically significant
• 00:35:08 – Overview of Complete Randomized Design, Block Design and Matched Pair Design
• 00:44:23 – Design and experiment using complete randomized design or a block design (Examples #9-10)
• 00:56:09 – Identify the response and explanatory variables, experimental units, lurking variables, and design an experiment to test a new drug (Example #11)
• Practice Problems with Step-by-Step Solutions
• Chapter Tests with Video Solutions

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3.4 - experimental and observational studies.

Now that Jaylen can weigh the different sampling strategies, he might want to consider the type of study he is conduction. As a note, for students interested in research designs, please consult STAT 503 for a much more in-depth discussion. However, for this example, we will simply distinguish between experimental and observational studies.

Now that we know how to collect data, the next step is to determine the type of study. The type of study will determine what type of relationship we can conclude.

There are predominantly two different types of studies: 

Let's say that there is an option to take quizzes throughout this class. In an  observational study , we may find that better students tend to take the quizzes and do better on exams. Consequently, we might conclude that there may be a relationship between quizzes and exam scores.

In an experimental study , we would randomly assign quizzes to specific students to look for improvements. In other words, we would look to see whether taking quizzes causes higher exam scores.

Causation Section  

It is very important to distinguish between observational and experimental studies since one has to be very skeptical about drawing cause and effect conclusions using observational studies. The use of random assignment of treatments (i.e. what distinguishes an experimental study from an observational study) allows one to employ cause and effect conclusions.

Ethics is an important aspect of experimental design to keep in mind. For example, the original relationship between smoking and lung cancer was based on an observational study and not an assignment of smoking behavior.

Introduction to Data Science I & II

Observational versus experimental studies, observational versus experimental studies #.

In most research questions or investigations, we are interested in finding an association that is causal (the first scenario in the previous section ). For example, “Is the COVID-19 vaccine effective?” is a causal question. The researcher is looking for an association between receiving the COVID-19 vaccine and contracting (symptomatic) COVID-19, but more specifically wants to show that the vaccine causes a reduction in COVID-19 infections (Baden et al., 2020) 1 .

Experimental Studies #

There are 3 necessary conditions for showing that a variable X (for example, vaccine) causes an outcome Y (such as not catching COVID-19):

Temporal Precedence : We must show that X (the cause) happened before Y (the effect).

Non-spuriousness : We must show that the effect Y was not seen by chance.

No alternate cause : We must show that no other variable accounts for the relationship between X and Y .

If any of the three is not present, the association cannot be causal. If the proposed cause did not happen before the effect, it cannot have caused the effect. In addition, if the effect was seen by chance and cannot be replicated, the association is spurious and therefore not causal. Lastly, if there is another phenomenon that accounts for the association seen, then it cannot be a causal association. These conditions are therefore, necessary to show causality.

The best way to show all three necessary conditions is by conducting an experiment . Experiments involve controllable factors which are measured and determined by the experimenter, uncontrollable factors which are measured but not determined by the experimentor, and experimental variability or noise which is unmeasured and uncontrolled. Controllable factors that the experimenter manipulates in his or her experiment are known as independent variables . In our vaccination example, the independent variable is receipt of vaccine. Uncontrollable factors that are hypothesized to depend on the independent variable are known as dependent variables. The dependent variable in the vaccination example is contraction of COVID-19. The experimentor cannot control whether participants catch the disease, but can measure it, and it is hypothesized that catching the disease is dependent on vaccination status.

Control Groups #

When conducting an experiment, it is important to have a comparison or control group . The control group is used to better understand the effect of the independent variable. For example, if all patients are given the vaccine, it would be impossible to measure whether the vaccine is effective as we would not know the outcome if patients had not received the vaccine. In order to measure the effect of the vaccine, the researcher must compare patients who did not receive the vaccine to patients that did receive the vaccine. This comparison group of patients who did not receive the vaccine is the control group for the experiment. The control group allows the researcher to view an effect or association. When scientists say that the COVID-19 vaccine is 94% effective, this does not mean that only 6% of people who got the vaccine in their study caught COVID-19 (the number is actually much lower!). That would not take into account the rate of catching COVID-19 for those without a vaccine. Rather, 94% effective refers to having 94% lower incidence of infection compared to the control group.

Let’s illustrate this using data from the efficacy trial by Baden and colleagues in 2020. In their primary analysis, 14,073 participants were in the placebo group and 14,134 in the vaccine group. Of these participants, a total of 196 were diagnosed with COVID-19 during the 78 day follow-up period: 11 in the vaccine group and 186 in the placebo group. This means, 0.08% of those in the vaccine group and 1.32% of those in the placebo group were diagnosed with COVID-19. Dividing 0.08 by 1.32, we see that the proportion of cases in the vaccine group was only 6% of the proportion of cases in the placebo group. Therefore, the vaccine is 94% effective.

Chicago has a population of almost 3,000,000. Extrapolating using the numbers from above, without the vaccine, 39,600 people would be expected to catch COVID-19 in the period between 14 and 92 days after their second vaccine. If everyone were vaccinated, the expected number would drop to 2,400. This is a large reduction! However, it is important that the researcher shows this effect is non-spurious and therefore important and significant. One way to do this is through replication : applying a treatment independently across two or more experimental subjects. In our example, researchers conducted many similar experiments for multiple groups of patients to show that the effect can be seen reliably.

Randomization #

A researcher must also be able to show there is no alternate cause for the association in order to prove causality. This can be done through randomization : random assignment of treatment to experimental subjects. Consider a group of patients where all male patients are given the treatment and all female patients are in the control group. If an association is found, it would be unclear whether this association is due to the treatment or the fact that the groups were of differing sex. By randomizing experimental subjects to groups, researchers ensure there is no systematic difference between groups other than the treatment and therefore no alternate cause for the relationship between treatment and outcome.

Another way of ensuring there is no alternate cause is by blocking : grouping similar experimental units together and assigning different treatments within such groups. Blocking is a way of dealing with sources of variability that are not of primary interest to the experimenter. For example, a researcher may block on sex by grouping males together and females together and assigning treatments and controls within the different groups. Best practices are to block the largest and most salient sources of variability and randomize what is difficult or impossible to block. In our example blocking would account for variability introduced by sex whereas randomization would account for factors of variability such as age or medical history which are more difficult to block.

Observational Studies #

Randomized experiments are considered the “Gold Standard” for showing a causal relationship. However, it is not always ethical or feasible to conduct a randomized experiment. Consider the following research question: Does living in Northern Chicago increase life expectancy? It would be infeasible to conduct an experiment which randomly allocates people to live in different parts of the city. Therefore, we must turn to observational data to test this question. Where experiments involve one or more variables controlled by the experimentor (dose of a drug for example), in observational studies there is no effort or intention to manipulate or control the object of study. Rather, researchers collect data without interfering with the subjects. For example, researchers may conduct a survey gathering both health and neighborhood data, or they may have access to administrative data from a local hospital. In these cases, the researchers are merely observing variables and outcomes.

There are two types of observational studies: retrospective studies and prospective studies. In a retrospective study , data is collected after events have taken place. This may be through surveys, historical data, or administrative records. An example of a retrospective study would be using administrative data from a hospital to study incidence of disease. In contrast, a prospective study identifies subjects beforehand and collects data as events unfold. For example, one might use a prospective study to evaluate how personality traits develop in children, by following a predetermined set of children through elementary school and giving them personality assessments each year.

Baden LR, El Sahly HM, Essink B, Kotloff K, Frey S, Novak R, Diemert D, Spector SA, Rouphael N, Creech CB, McGettigan J. Efficacy and safety of the mRNA-1273 SARS-CoV-2 vaccine. New England journal of medicine. 2020 Dec 30.

Experimental Studies and Observational Studies

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Experimental studies: Experiments, Randomized controlled trials (RCTs) ; Observational studies: Non-experimental studies, Non-manipulation studies, Naturalistic studies

Definitions

The experimental study is a powerful methodology for testing causal relations between one or more explanatory variables (i.e., independent variables) and one or more outcome variables (i.e., dependent variable). In order to accomplish this goal, experiments have to meet three basic criteria: (a) experimental manipulation (variation) of the independent variable(s), (b) randomization – the participants are randomly assigned to one of the experimental conditions, and (c) experimental control for the effect of third variables by eliminating them or keeping them constant.

In observational studies, investigators observe or assess individuals without manipulation or intervention. Observational studies are used for assessing the mean levels, the natural variation, and the structure of variables, as well as...

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Pinquart, M. (2021). Experimental Studies and Observational Studies. In: Gu, D., Dupre, M.E. (eds) Encyclopedia of Gerontology and Population Aging. Springer, Cham. https://doi.org/10.1007/978-3-030-22009-9_573

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Section 1.2: Observational Studies versus Designed Experiments

• 1.1 Introduction to the Practice of Statistics
• 1.2 Observational Studies versus Designed Experiments
• 1.3 Random Sampling
• 1.4 Bias in Sampling
• 1.5 The Design of Experiments

By the end of this lesson, you will be able to...

• distinguish between an observational study and a designed experiment
• identify possible lurking variables
• explain the various types of observational studies

For a quick overview of this section, watch this short video summary:

To begin, we're going to discuss some of the ways to collect data. In general, there are a few standards:

• existing sources
• survey sampling
• designed experiments

Most of us associate the word census with the U.S. Census, but it actually has a broader definition. Here's typical definition:

A census is a list of all individuals in a population along with certain characteristics of each individual.

The nice part about a census is that it gives us all the information we want. Of course, it's usually impossible to get - imagine trying to interview every single ECC student . That'd be over 10,000 interviews!

So if we can't get a census, what do we do? A great source of data is other studies that have already been completed. If you're trying to answer a particular question, look to see if someone else has already collected data about that population. The moral of the story is this: Don't collect data that have already been collected!

Observational Studies versus Designed Experiments

Now to one of the main objectives for this section. Two other very common sources of data are observational studies and designed experiments . We're going to take some time here to describe them and distinguish between them - you'll be expected to be able to do the same in homework and on your first exam.

The easiest examples of observational studies are surveys. No attempt is made to influence anything - just ask questions and record the responses. By definition,

An observational study measures the characteristics of a population by studying individuals in a sample, but does not attempt to manipulate or influence the variables of interest.

For a good example, try visiting the Pew Research Center . Just click on any article and you'll see an example of an observational study. They just sample a particular group and ask them questions.

In contrast, designed experiments explicitly do attempt to influence results. They try to determine what affect a particular treatment has on an outcome.

A designed experiment applies a treatment to individuals (referred to as experimental units or subjects ) and attempts to isolate the effects of the treatment on a response variable .

For a nice example of a designed experiment, check out this article from National Public Radio about the effect of exercise on fitness.

So let's look at a couple examples.

Visit this link from Science Daily , from July 8th, 2008. It talks about the relationship between Post-Traumatic Stress Disorder (PTSD) and heart disease. After reading the article carefully, try to decide whether it was an observational study or a designed experiment

What was it?

This was a tricky one. It was actually an observational study . The key is that the researchers didn't force the veterans to have PTSD, they simply observed the rate of heart disease for those soldiers who have PTSD and the rate for those who do not.

Visit this link from the Gallup Organization , from June 17th, 2008. It looks at what Americans' top concerns were at that point. Read carefully and think of the how the data were collected. Do you think this was an observational study or a designed experiment? Why?

Think carefully about which you think it was, and just as important - why? When you're ready, click the link below.

If you were thinking that this was an observational study , you were right!The key here is that the individuals sampled were just asked what was important to them. The study didn't try to impose certain conditions on people for a set amount of time and see if those conditions affected their responses.

This last example is regarding the "low-carb" Atkins diet, and how it compares with other diets. Read through this summary of a report in the New England Journal of Medicine and see if you can figure out whether it's an observational study or a designed experiment.

As expected, this was a designed experiment , but do you know why? The key here is they forced individuals to maintain a certain diet, and then compared the participants' health at the end.

Probably the biggest difference between observational studies and designed experiments is the issue of association versus causation . Since observational studies don't control any variables, the results can only be associations . Because variables are controlled in a designed experiment, we can have conclusions of causation .

Look back over the three examples linked above and see if all three reported their results correctly. You'll often find articles in newspapers or online claiming one variable caused a certain response in another, when really all they had was an association from doing an observational study.

The discussion of the differences between observational studies and designed experiments may bring up an interesting question - why are we worried so much about the difference?

We already mentioned the key at the end of the previous page, but it bears repeating here:

Observational studies only allow us to claim association ,not causation .

The primary reason behind this is something called a lurking variable (sometimes also termed a confounding factor , among other similar terms).

A lurking variable is a variable that affects both of the variables of interest, but is either not known or is not acknowledged.

Consider the following example, from The Washington Post:

Coffee may have health benefits and may not pose health risks for many people

By Carolyn Butler Tuesday, December 22, 2009

Of all the relationships in my life, by far the most on-again, off-again has been with coffee: From that initial, tentative dalliance in college to a serious commitment during my first real reporting job to breaking up altogether when I got pregnant, only to fail miserably at quitting my daily latte the second time I was expecting. More recently the relationship has turned into full-blown obsession and, ironically, I often fall asleep at night dreaming of the delicious, satisfying cup of joe that awaits, come morning.

[...] Rest assured: Not only has current research shown that moderate coffee consumption isn't likely to hurt you, it may actually have significant health benefits. "Coffee is generally associated with a less health-conscious lifestyle -- people who don't sleep much, drink coffee, smoke, drink alcohol," explains Rob van Dam, an assistant professor in the departments of nutrition and epidemiology at the Harvard School of Public Health. He points out that early studies failed to account for such issues and thus found a link between drinking coffee and such conditions as heart disease and cancer, a link that has contributed to java's lingering bad rep. "But as more studies have been conducted-- larger and better studies that controlled for healthy lifestyle issues --the totality of efforts suggests that coffee is a good beverage choice."

Source: Washington Post

What is this article telling us? If you look at the parts in bold, you can see that Professor van Dam is describing a lurking variable: lifestyle. In past studies, this variable wasn't accounted for. Researchers in the past saw the relationship between coffee and heart disease, and came to the conclusion that the coffee was causing the heart disease.

But since those were only observational studies, the researchers could only claim an association . In that example, the lifestyle choices of individuals was affecting both their coffee use and other risks leading to heart disease. So "lifestyle" would be an example of a lurking variable in that example.

For more on lurking variables, check out this link from The Math Forum and this one from The Psychology Wiki . Both give further examples and illustrations.

With all the problems of lurking variables, there are many good reasons to do an observational study. For one, a designed experiment may be impractical or even unethical (imagine a designed experiment regarding the risks of smoking). Observational studies also tend to cost much less than designed experiments, and it's often possible to obtain a much larger data set than you would with a designed experiment. Still, it's always important to remember the difference in what we can claim as a result of observational studies versus designed experiments.

Types of Observational Studies

There are three major types of observational studies, and they're listed in your text: cross-sectional studies, case-control studies, and cohort studies.

Cross-sectional Studies

This first type of observational study involves collecting data about individuals at a certain point in time. A researcher concerned about the effect of working with asbestos might compare the cancer rate of those who work with asbestos versus those who do not.

Cross-sectional studies are cheap and easy to do, but they don't give very strong results. In our quick example, we can't be sure that those working with asbestos who don't report cancer won't eventually develop it. This type of study only gives a bit of the picture, so it is rarely used by itself. Researchers tend to use a cross-sectional study to first determine if their might be a link, and then later do another study (like one of the following) to further investigate.

Case-control Studies

Case-control studies are frequently used in the medical community to compare individuals with a particular characteristic (this group is the case )with individuals who do not have that characteristic (this group is the control ). Researchers attempt to select homogeneous groups, so that on average, all other characteristics of the individuals will be similar, with only the characteristic in question differing.

One of the most famous examples of this type of study is the early research on the link between smoking and lung cancer in the United Kingdom by Richard Doll and A. Bradford Hill. In the 1950's, almost 80% of adults in the UK were smokers, and the connection between smoking and lung cancer had not yet been established. Doll and Hill interviewed about 700 lung cancer patients to try to determine a possible cause.

This type of study is retrospective ,because it asks the individuals to look back and describe their habits(regarding smoking, in this case). There are clear weaknesses in a study like this, because it expects individuals to not only have an accurate memory, but also to respond honestly. (Think about a study concerning drug use and cognitive impairment.) Not only that, we discussed previously that such a study may prove association , but it cannot prove causation .

Cohort Studies

A cohort describes a group of individuals, and so a cohort study is one in which a group of individuals is selected to participate in a study. The group is then observed over a period of time to determine if particular characteristics affect a response variable.

Based on their earlier research, Doll and Hill began one of the largest cohort studies in 1951. The study was again regarding the link between smoking and lung cancer. The study began with 34,439 male British doctors, and followed them for over 50 years. Doll and Hill first reported findings in 1954 in the British Medical Journal , and then continued to report their findings periodically afterward. Their last report was in 2004,again published in the British Medical Journal . This last report reflected on 50 years of observational data from the cohort.

This last type of study is called prospective , because it begins with the group and then collects data over time. Cohort studies are definitely the most powerful of the observational studies,particularly with the quantity and quality of data in a study like the previous one.

Let's look at some examples.

A recent article in the BBC News Health section described a study concerning dementia and "mid-life ills". According to the article, researches followed more than 11,000 people over a period of 12-14 years. They found that smoking, diabetes, and high blood pressure were all factors in the onset of dementia.

What type of observational study was this? Cross-sectional, case-control,or cohort?

Because the researchers tracked the 11,000 participants, this is a cohort study .

In 1993, the National Institute of Environmental Health Sciences funded a study in Iowa regarding the possible relationship between radon levels and the incidence of cancer. The study gathered information from 413 participants who had developed lung cancer and compared those results with 614 participants who did not have lung cancer.

What type of study was this?

This study was retrospective - gathering information about the group of interest (those with cancer) and comparing them with a control group(those without cancer). This is an example of a case-control study .

Thought his may seem similar to a cross-sectional study, it differs in that the individuals are "matched" (with cancer vs. without cancer)and the individuals are expected to look back in time and describe their time spent in the home to determine their radon exposure.

In 2004, researchers published an article in the New England Journal of Medicine regarding the relationship between the mental health of soldiers exposed to combat stress. The study collected information from soldiers in four combat infantry units either before their deployment to Iraq or three to four months after their return from combat duty.

Since this was simply a survey given over a short period of time to try to examine the effect of combat duty, this was a cross-sectional study. Unlike the previous example, it did not ask the participants to delve into their history, nor did it explicitly "match" soldiers with a particular characteristic.

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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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Statistics By Jim

Making statistics intuitive

What is an Observational Study: Definition & Examples

By Jim Frost 10 Comments

What is an Observational Study?

An observational study uses sample data to find correlations in situations where the researchers do not control the treatment, or independent variable, that relates to the primary research question. The definition of an observational study hinges on the notion that the researchers only observe subjects and do not assign them to the control and treatment groups. That’s the key difference between an observational study vs experiment. These studies are also known as quasi-experiments and correlational studies .

True experiments assign subject to the experimental groups where the researchers can manipulate the conditions. Unfortunately, random assignment is not always possible. For these cases, you can conduct an observational study.

In this post, learn about the types of observational studies, why they are susceptible to confounding variables, and how they compare to experiments. I’ll close this post by reviewing a published observational study about vitamin supplement usage.

Observational Study Definition

In an observational study, the researchers only observe the subjects and do not interfere or try to influence the outcomes. In other words, the researchers do not control the treatments or assign subjects to experimental groups. Instead, they observe and measure variables of interest and look for relationships between them. Usually, researchers conduct observational studies when it is difficult, impossible, or unethical to assign study participants to the experimental groups randomly. If you can’t randomly assign subjects to the treatment and control groups, then you observe the subjects in their self-selected states.

Observational Study vs Experiment

Randomized experiments provide better results than observational studies. Consequently, you should always use a randomized experiment whenever possible. However, if randomization is not possible, science should not come to a halt. After all, we still want to learn things, discover relationships, and make discoveries. For these cases, observational studies are a good alternative to a true experiment. Let’s compare the differences between an observational study vs. an experiment.

Random assignment in an experiment reduces systematic differences between experimental groups at the beginning of the study, which increases your confidence that the treatments caused any differences between groups you observe at the end of the study. In contrast, an observational study uses self-formed groups that can have pre-existing differences, which introduces the problem of confounding variables. More on that later!

In a randomized experiment, randomization tends to equalize confounders between groups and, thereby, prevents problems. In my post about random assignment , I describe that process as an elegant solution for confounding variables. You don’t need to measure or even know which variables are confounders, and randomization will still mitigate their effects. Additionally, you can use control variables in an experiment to keep the conditions as consistent as possible. For more detail about the differences, read Observational Study vs. Experiment .

If you’re looking for a middle ground choice between observational studies vs experiments, consider using a quasi-experimental design. These methods don’t require you to randomly assign participants to the experimental groups and still allow you to draw better causal conclusions about an intervention than an observational study. Learn more about Quasi-Experimental Design Overview & Examples .

Related posts : Experimental Design: Definition and Examples , Randomized Controlled Trials (RCTs) , and Control Groups in Experiments

Observational Study Examples

Consider using an observational study when random assignment for an experiment is problematic. This approach allows us to proceed and draw conclusions about effects even though we can’t control the independent variables. The following observational study examples will help you understand when and why to use them.

For example, if you’re studying how depression affects performance of an activity, it’s impossible to assign subjects to the depression and control group randomly. However, you can have subjects with and without depression perform the activity and compare the results in an observational study.

Or imagine trying to assign subjects to cigarette smoking and non-smoking groups randomly?! However, you can observe people in both groups and assess the differences in health outcomes in an observational study.

Suppose you’re studying a treatment for a disease. Ideally, you recruit a group of patients who all have the disease, and then randomly assign them to the treatment and control group. However, it’s unethical to withhold the treatment, which rules out a control group. Instead, you can compare patients who voluntarily do not use the medicine to those who do use it.

In all these observational study examples, the researchers do not assign subjects to the experimental groups. Instead, they observe people who are already in these groups and compare the outcomes. Hence, the scientists must use an observational study vs. an experiment.

Types of Observational Studies

The observational study definition states that researchers only observe the outcomes and do not manipulate or control factors . Despite this limitation, there various types of observational studies.

The following experimental designs are three standard types of observational studies.

• Cohort Study : A longitudinal observational study that follows a group who share a defining characteristic. These studies frequently determine whether exposure to risk factor affects an outcome over time.
• Case-Control Study : A retrospective observational study that compares two existing groups—the case group with the condition and the control group without it. Researchers compare the groups looking for potential risk factors for the condition.
• Cross-Sectional Study : Takes a snapshot of a moment in time so researchers can understand the prevalence of outcomes and correlations between variables at that instant.

Qualitative research studies are usually observational in nature, but they collect non-numeric data and do not perform statistical analyses.

Retrospective studies must be observational.

Later in this post, we’ll closely examine a quantitative observational study example that assesses vitamin supplement consumption and how that affects the risk of death. It’s possible to use random assignment to place each subject in either the vitamin treatment group or the control group. However, the study assesses vitamin consumption in 40,000 participants over the course of two decades. It’s unrealistic to enforce the treatment and control protocols over such a long time for so many people!

Drawbacks of Observational Studies

While observational studies get around the inability to assign subjects randomly, this approach opens the door to the problem of confounding variables. A confounding variable, or confounder, correlates with both the experimental groups and the outcome variable. Because there is no random process that equalizes the experimental groups in an observational study, confounding variables can systematically differ between groups when the study begins. Consequently, confounders can be the actual cause for differences in outcome at the end of the study rather than the primary variable of interest. If an experiment does not account for confounding variables, confounders can bias the results and create spurious correlations .

Performing an observational study can decrease the internal validity of your study but increase the external validity. Learn more about internal and external validity .

Let’s see how this works. Imagine an observational study that compares people who take vitamin supplements to those who do not. People who use vitamin supplements voluntarily will tend to have other healthy habits that exist at the beginning of the study. These healthy habits are confounding variables. If there are differences in health outcomes at the end of the study, it’s possible that these healthy habits actually caused them rather than the vitamin consumption itself. In short, confounders confuse the results because they provide alternative explanations for the differences.

Despite the limitations, an observational study can be a valid approach. However, you must ensure that your research accounts for confounding variables. Fortunately, there are several methods for doing just that!

Learn more about Correlation vs. Causation: Understanding the Differences .

Accounting for Confounding Variables in an Observational Study

Because observational studies don’t use random assignment, confounders can be distributed disproportionately between conditions. Consequently, experimenters need to know which variables are confounders, measure them, and then use a method to account for them. It involves more work, and the additional measurements can increase the costs. And there’s always a chance that researchers will fail to identify a confounder, not account for it, and produce biased results. However, if randomization isn’t an option, then you probably need to consider an observational study.

Trait matching and statistically controlling confounders using multivariate procedures are two standard approaches for incorporating confounding variables.

Related post : Causation versus Correlation in Statistics

Matching in Observational Studies

Matching is a technique that involves selecting study participants with similar characteristics outside the variable of interest or treatment. Rather than using random assignment to equalize the experimental groups, the experimenters do it by matching observable characteristics. For every participant in the treatment group, the researchers find a participant with comparable traits to include in the control group. Matching subjects facilitates valid comparisons between those groups. The researchers use subject-area knowledge to identify characteristics that are critical to match.

For example, a vitamin supplement study using matching will select subjects who have similar health-related habits and attributes. The goal is that vitamin consumption will be the primary difference between the groups, which helps you attribute differences in health outcomes to vitamin consumption. However, the researchers are still observing participants who decide whether they consume supplements.

Matching has some drawbacks. The experimenters might not be aware of all the relevant characteristics they need to match. In other words, the groups might be different in an essential aspect that the researchers don’t recognize. For example, in the hypothetical vitamin study, there might be a healthy habit or attribute that affects the outcome that the researchers don’t measure and match. These unmatched characteristics might cause the observed differences in outcomes rather than vitamin consumption.

Learn more about Matched Pairs Design: Uses & Examples .

Using Multiple Regression in Observational Studies

Random assignment and matching use different methods to equalize the experimental groups in an observational study. However, statistical techniques, such as multiple regression analysis , don’t try to equalize the groups but instead use a model that accounts for confounding variables. These studies statistically control for confounding variables.

In multiple regression analysis, including a variable in the model holds it constant while you vary the variable/treatment of interest. For information about this property, read my post When Should I Use Regression Analysis?

As with matching, the challenge is to identify, measure, and include all confounders in the regression model. Failure to include a confounding variable in a regression model can cause omitted variable bias to distort your results.

Next, we’ll look at a published observational study that uses multiple regression to account for confounding variables.

Related post : Independent and Dependent Variables in a Regression Model

Vitamin Supplement Observational Study Example

Murso et al. (2011)* use a longitudinal observational study that ran 22 years to assess differences in death rates for subjects who used vitamin supplements regularly compared to those who did not use them. This study used surveys to record the characteristics of approximately 40,000 participants. The surveys asked questions about potential confounding variables such as demographic information, food intake, health details, physical activity, and, of course, supplement intake.

Because this is an observational study, the subjects decided for themselves whether they were taking vitamin supplements. Consequently, it’s safe to assume that supplement users and non-users might be different in other ways. From their article, the researchers found the following pre-existing differences between the two groups:

Supplement users had a lower prevalence of diabetes mellitus, high blood pressure, and smoking status; a lower BMI and waist to hip ratio, and were less likely to live on a farm. Supplement users had a higher educational level, were more physically active and were more likely to use estrogen replacement therapy. Also, supplement users were more likely to have a lower intake of energy, total fat, and monounsaturated fatty acids, saturated fatty acids and to have a higher intake of protein, carbohydrates, polyunsaturated fatty acids, alcohol, whole grain products, fruits, and vegetables.

Whew! That’s a long list of differences! Supplement users were different from non-users in a multitude of ways that are likely to affect their risk of dying. The researchers must account for these confounding variables when they compare supplement users to non-users. If they do not, their results can be biased.

This example illustrates a key difference between an observational study vs experiment. In a randomized experiment, the randomization would have equalized the characteristics of those the researchers assigned to the treatment and control groups. Instead, the study works with self-sorted groups that have numerous pre-existing differences!

Using Multiple Regression to Statistically Control for Confounders

To account for these initial differences in the vitamin supplement observational study, the researchers use regression analysis and include the confounding variables in the model.

The researchers present three regression models. The simplest model accounts only for age and caloric intake. Next, are two models that include additional confounding variables beyond age and calories. The first model adds various demographic information and seven health measures. The second model includes everything in the previous model and adds several more specific dietary intake measures. Using statistical significance as a guide for specifying the correct regression model , the researchers present the model with the most variables as the basis for their final results.

It’s instructive to compare the raw results and the final regression results.

Raw results

The raw differences in death risks for consumers of folic acid, vitamin B6, magnesium, zinc, copper, and multivitamins are NOT statistically significant. However, the raw results show a significant reduction in the death risk for users of B complex, C, calcium, D, and E.

However, those are the raw results for the observational study, and they do not control for the long list of differences between the groups that exist at the beginning of the study. After using the regression model to control for the confounding variables statistically, the results change dramatically.

Adjusted results

Of the 15 supplements that the study tracked in the observational study, researchers found consuming seven of these supplements were linked to a statistically significant INCREASE in death risk ( p-value < 0.05): multivitamins (increase in death risk 2.4%), vitamin B6 (4.1%), iron (3.9%), folic acid (5.9%), zinc (3.0%), magnesium (3.6%), and copper (18.0%). Only calcium was associated with a statistically significant reduction in death risk of 3.8%.

In short, the raw results suggest that those who consume supplements either have the same or lower death risks than non-consumers. However, these results do not account for the multitude of healthier habits and attributes in the group that uses supplements.

In fact, these confounders seem to produce most of the apparent benefits in the raw results because, after you statistically control the effects of these confounding variables, the results worsen for those who consume vitamin supplements. The adjusted results indicate that most vitamin supplements actually increase your death risk!

This research illustrates the differences between an observational study vs experiment. Namely how the pre-existing differences between the groups allow confounders to bias the raw results, making the vitamin consumption outcomes look better than they really are.

In conclusion, if you can’t randomly assign subjects to the experimental groups, an observational study might be right for you. However, be aware that you’ll need to identify, measure, and account for confounding variables in your experimental design.

Jaakko Mursu, PhD; Kim Robien, PhD; Lisa J. Harnack, DrPH, MPH; Kyong Park, PhD; David R. Jacobs Jr, PhD; Dietary Supplements and Mortality Rate in Older Women: The Iowa Women’s Health Study ; Arch Intern Med . 2011;171(18):1625-1633.

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December 30, 2023 at 5:05 am

I see, but our professor required us to indicate what year it was put into the article. May you tell me what year was this published originally? <3

December 30, 2023 at 3:40 pm

December 29, 2023 at 10:46 am

Hi, may I use your article as a citation for my thesis paper? If so, may I know the exact date you published this article? Thank you!

December 29, 2023 at 2:13 pm

Definitely feel free to cite this article! 🙂

When citing online resources, you typically use an “Accessed” date rather than a publication date because online content can change over time. For more information, read Purdue University’s Citing Electronic Resources .

November 18, 2021 at 10:09 pm

Love your content and has been very helpful!

Can you please advise the question below using an observational data set:

I have three years of observational GPS data collected on athletes (2019/2020/2021). Approximately 14-15 athletes per game and 8 games per year. The GPS software outputs 50+ variables for each athlete in each game, which we have narrowed down to 16 variables of interest from previous research.

2 factors 1) Period (first half, second half, and whole game), 2) Position (two groups with three subgroups in each – forwards (group 1, group 2, group 3) and backs (group 1, group 2, group 3))

16 variables of interest – all numerical and scale variables. Some of these are correlated, but not all.

My understanding is that I can use a oneway ANOVA for each year on it’s own, using one factor at a time (period or position) with post hoc analysis. This is fine, if data meets assumptions and is normally distributed. This tells me any significant interactions between variables of interest with chosen factor. For example, with position factor, do forwards in group 1 cover more total running distance than forwards in group 2 or backs in group 3.

However, I want to go deeper with my analysis. If I want to see if forwards in group 1 cover more total running distance in period 1 than backs in group 3 in the same period, I need an additional factor and the oneway ANOVA does not suit. Therefore I can use a twoway ANOVA instead of 2 oneway ANOVA’s and that solves the issue, correct?

This is complicated further by looking to compare 2019 to 2020 or 2019 to 2021 to identify changes over time, which would introduce a third independent variable.

I believe this would require a threeway ANOVA for this observational data set. 3 factors – Position, Period, and Year?

Are there any issues or concerns you see at first glance?

I appreciate your time and consideration.

April 12, 2021 at 2:02 pm

Could an observational study use a correlational design.

e.g. measuring effects of two variables on happiness, if you’re not intervening.

April 13, 2021 at 12:14 am

Typically, with observational studies, you’d want to include potential confounders, etc. Consequently, I’ve seen regression analysis used more frequently for observational studies to be able to control for other things because you’re not using randomization. You could use correlation to observe the relationship. However, you wouldn’t be controlling for potential confounding variables. Just something to consider.

April 11, 2021 at 1:28 pm

Hi, If I am to administer moderate doses of coffee for a hypothetical experiment, does it raise ethical concerns? Can I use random assignment for it?

April 11, 2021 at 4:06 pm

I don’t see any inherent ethical problems here as long as you describe the participant’s experience in the experiment including the coffee consumption. They key with human subjects is “informed consent.” They’re agreeing to participate based on a full and accurate understanding of what participation involves. Additionally, you as a researcher, understand the process well enough to be able to ensure their safety.

In your study, as long as subject know they’ll be drinking coffee and agree to that, I don’t see a problem. It’s a proven safe substance for the vast majority of people. If potential subjects are aware of the need to consume coffee, they can determine whether they are ok with that before agreeing to participate.

June 17, 2019 at 4:51 am

Really great article which explains observational and experimental study very well. It presents broad picture with the case study which helped a lot in understanding the core concepts. Thanks

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Data for statistical studies are obtained by conducting either experiments or surveys. Experimental design is the branch of statistics that deals with the design and analysis of experiments. The methods of experimental design are widely used in the fields of agriculture, medicine , biology , marketing research, and industrial production.

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In an experimental study, variables of interest are identified. One or more of these variables, referred to as the factors of the study , are controlled so that data may be obtained about how the factors influence another variable referred to as the response variable , or simply the response. 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 .

Three of the more widely used experimental designs are the completely randomized design, the randomized block design, and the factorial design. In a completely randomized experimental design, the treatments are randomly assigned to the experimental units. For instance, applying this design method to the cholesterol-level study, the three types of exercise program (treatment) would be randomly assigned to the experimental units (patients).

The use of a completely randomized design will yield less precise results when factors not accounted for by the experimenter affect the response variable. Consider, for example, an experiment designed to study the effect of two different gasoline additives on the fuel efficiency , measured in miles per gallon (mpg), of full-size automobiles produced by three manufacturers. Suppose that 30 automobiles, 10 from each manufacturer, were available for the experiment. In a completely randomized design the two gasoline additives (treatments) would be randomly assigned to the 30 automobiles, with each additive being assigned to 15 different cars. Suppose that manufacturer 1 has developed an engine that gives its full-size cars a higher fuel efficiency than those produced by manufacturers 2 and 3. A completely randomized design could, by chance , assign gasoline additive 1 to a larger proportion of cars from manufacturer 1. In such a case, gasoline additive 1 might be judged to be more fuel efficient when in fact the difference observed is actually due to the better engine design of automobiles produced by manufacturer 1. To prevent this from occurring, a statistician could design an experiment in which both gasoline additives are tested using five cars produced by each manufacturer; in this way, any effects due to the manufacturer would not affect the test for significant differences due to gasoline additive. In this revised experiment, each of the manufacturers is referred to as a block, and the experiment is called a randomized block design. In general, blocking is used in order to enable comparisons among the treatments to be made within blocks of homogeneous experimental units.

Factorial experiments are designed to draw conclusions about more than one factor, or variable. The term factorial is used to indicate that all possible combinations of the factors are considered. For instance, if there are two factors with a levels for factor 1 and b levels for factor 2, the experiment will involve collecting data on a b treatment combinations. The factorial design can be extended to experiments involving more than two factors and experiments involving partial factorial designs.

A computational procedure frequently used to analyze the data from an experimental study employs a statistical procedure known as the analysis of variance. For a single-factor experiment, this procedure uses a hypothesis test concerning equality of treatment means to determine if the factor has a statistically significant effect on the response variable. For experimental designs involving multiple factors, a test for the significance of each individual factor as well as interaction effects caused by one or more factors acting jointly can be made. Further discussion of the analysis of variance procedure is contained in the subsequent section.

Regression and correlation analysis

Regression analysis involves identifying the relationship between a dependent variable and one or more independent variables . A model of the relationship is hypothesized, and estimates of the parameter values are used to develop an estimated regression equation . Various tests are then employed to determine if the model is satisfactory. If the model is deemed satisfactory, the estimated regression equation can be used to predict the value of the dependent variable given values for the independent variables.

In simple linear regression , the model used to describe the relationship between a single dependent variable y and a single independent variable x is y = β 0 + β 1 x + ε. β 0 and β 1 are referred to as the model parameters, and ε is a probabilistic error term that accounts for the variability in y that cannot be explained by the linear relationship with x . If the error term were not present, the model would be deterministic; in that case, knowledge of the value of x would be sufficient to determine the value of y .

In multiple regression analysis , the model for simple linear regression is extended to account for the relationship between the dependent variable y and p independent variables x 1 , x 2 , . . ., x p . The general form of the multiple regression model is y = β 0 + β 1 x 1 + β 2 x 2 + . . . + β p x p + ε. The parameters of the model are the β 0 , β 1 , . . ., β p , and ε is the error term.

Either a simple or multiple regression model is initially posed as a hypothesis concerning the relationship among the dependent and independent variables. The least squares method is the most widely used procedure for developing estimates of the model parameters. For simple linear regression, the least squares estimates of the model parameters β 0 and β 1 are denoted b 0 and b 1 . Using these estimates, an estimated regression equation is constructed: ŷ = b 0 + b 1 x . The graph of the estimated regression equation for simple linear regression is a straight line approximation to the relationship between y and x .

As an illustration of regression analysis and the least squares method, suppose a university medical centre is investigating the relationship between stress and blood pressure . Assume that both a stress test score and a blood pressure reading have been recorded for a sample of 20 patients. The data are shown graphically in Figure 4 , called a scatter diagram . Values of the independent variable, stress test score, are given on the horizontal axis, and values of the dependent variable, blood pressure, are shown on the vertical axis. The line passing through the data points is the graph of the estimated regression equation: ŷ = 42.3 + 0.49 x . The parameter estimates, b 0 = 42.3 and b 1 = 0.49, were obtained using the least squares method.

A primary use of the estimated regression equation is to predict the value of the dependent variable when values for the independent variables are given. For instance, given a patient with a stress test score of 60, the predicted blood pressure is 42.3 + 0.49(60) = 71.7. The values predicted by the estimated regression equation are the points on the line in Figure 4 , and the actual blood pressure readings are represented by the points scattered about the line. The difference between the observed value of y and the value of y predicted by the estimated regression equation is called a residual . The least squares method chooses the parameter estimates such that the sum of the squared residuals is minimized.

A commonly used measure of the goodness of fit provided by the estimated regression equation is the coefficient of determination . Computation of this coefficient is based on the analysis of variance procedure that partitions the total variation in the dependent variable, denoted SST, into two parts: the part explained by the estimated regression equation, denoted SSR, and the part that remains unexplained, denoted SSE.

The measure of total variation, SST, is the sum of the squared deviations of the dependent variable about its mean: Σ( y − ȳ ) 2 . This quantity is known as the total sum of squares. The measure of unexplained variation, SSE, is referred to as the residual sum of squares. For the data in Figure 4 , SSE is the sum of the squared distances from each point in the scatter diagram (see Figure 4 ) to the estimated regression line: Σ( y − ŷ ) 2 . SSE is also commonly referred to as the error sum of squares. A key result in the analysis of variance is that SSR + SSE = SST.

The ratio r 2 = SSR/SST is called the coefficient of determination. If the data points are clustered closely about the estimated regression line, the value of SSE will be small and SSR/SST will be close to 1. Using r 2 , whose values lie between 0 and 1, provides a measure of goodness of fit; values closer to 1 imply a better fit. A value of r 2 = 0 implies that there is no linear relationship between the dependent and independent variables.

When expressed as a percentage , the coefficient of determination can be interpreted as the percentage of the total sum of squares that can be explained using the estimated regression equation. For the stress-level research study, the value of r 2 is 0.583; thus, 58.3% of the total sum of squares can be explained by the estimated regression equation ŷ = 42.3 + 0.49 x . For typical data found in the social sciences, values of r 2 as low as 0.25 are often considered useful. For data in the physical sciences, r 2 values of 0.60 or greater are frequently found.

In a regression study, hypothesis tests are usually conducted to assess the statistical significance of the overall relationship represented by the regression model and to test for the statistical significance of the individual parameters. The statistical tests used are based on the following assumptions concerning the error term: (1) ε is a random variable with an expected value of 0, (2) the variance of ε is the same for all values of x , (3) the values of ε are independent, and (4) ε is a normally distributed random variable.

The mean square due to regression, denoted MSR, is computed by dividing SSR by a number referred to as its degrees of freedom ; in a similar manner, the mean square due to error, MSE , is computed by dividing SSE by its degrees of freedom. An F-test based on the ratio MSR/MSE can be used to test the statistical significance of the overall relationship between the dependent variable and the set of independent variables. In general, large values of F = MSR/MSE support the conclusion that the overall relationship is statistically significant. If the overall model is deemed statistically significant, statisticians will usually conduct hypothesis tests on the individual parameters to determine if each independent variable makes a significant contribution to the model.

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2.5: Experimental and Non-experimental Research

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• Danielle Navarro
• University of New South Wales

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One of the big distinctions that you should be aware of is the distinction between “experimental research” and “non-experimental research”. When we make this distinction, what we’re really talking about is the degree of control that the researcher exercises over the people and events in the study.

Experimental research

The key features of experimental research is that the researcher controls all aspects of the study, especially what participants experience during the study. In particular, the researcher manipulates or varies the predictor variables (IVs), and then allows the outcome variable (DV) to vary naturally. The idea here is to deliberately vary the predictors (IVs) to see if they have any causal effects on the outcomes. Moreover, in order to ensure that there’s no chance that something other than the predictor variables is causing the outcomes, everything else is kept constant or is in some other way “balanced” to ensure that they have no effect on the results. In practice, it’s almost impossible to think of everything else that might have an influence on the outcome of an experiment, much less keep it constant. The standard solution to this is randomisation: that is, we randomly assign people to different groups, and then give each group a different treatment (i.e., assign them different values of the predictor variables). We’ll talk more about randomisation later in this course, but for now, it’s enough to say that what randomisation does is minimise (but not eliminate) the chances that there are any systematic difference between groups.

Let’s consider a very simple, completely unrealistic and grossly unethical example. Suppose you wanted to find out if smoking causes lung cancer. One way to do this would be to find people who smoke and people who don’t smoke, and look to see if smokers have a higher rate of lung cancer. This is not a proper experiment, since the researcher doesn’t have a lot of control over who is and isn’t a smoker. And this really matters: for instance, it might be that people who choose to smoke cigarettes also tend to have poor diets, or maybe they tend to work in asbestos mines, or whatever. The point here is that the groups (smokers and non-smokers) actually differ on lots of things, not just smoking. So it might be that the higher incidence of lung cancer among smokers is caused by something else, not by smoking per se. In technical terms, these other things (e.g. diet) are called “confounds”, and we’ll talk about those in just a moment.

In the meantime, let’s now consider what a proper experiment might look like. Recall that our concern was that smokers and non-smokers might differ in lots of ways. The solution, as long as you have no ethics, is to control who smokes and who doesn’t. Specifically, if we randomly divide participants into two groups, and force half of them to become smokers, then it’s very unlikely that the groups will differ in any respect other than the fact that half of them smoke. That way, if our smoking group gets cancer at a higher rate than the non-smoking group, then we can feel pretty confident that (a) smoking does cause cancer and (b) we’re murderers.

Non-experimental research

Non-experimental research is a broad term that covers “any study in which the researcher doesn’t have quite as much control as they do in an experiment”. Obviously, control is something that scientists like to have, but as the previous example illustrates, there are lots of situations in which you can’t or shouldn’t try to obtain that control. Since it’s grossly unethical (and almost certainly criminal) to force people to smoke in order to find out if they get cancer, this is a good example of a situation in which you really shouldn’t try to obtain experimental control. But there are other reasons too. Even leaving aside the ethical issues, our “smoking experiment” does have a few other issues. For instance, when I suggested that we “force” half of the people to become smokers, I must have been talking about starting with a sample of non-smokers, and then forcing them to become smokers. While this sounds like the kind of solid, evil experimental design that a mad scientist would love, it might not be a very sound way of investigating the effect in the real world. For instance, suppose that smoking only causes lung cancer when people have poor diets, and suppose also that people who normally smoke do tend to have poor diets. However, since the “smokers” in our experiment aren’t “natural” smokers (i.e., we forced non-smokers to become smokers; they didn’t take on all of the other normal, real life characteristics that smokers might tend to possess) they probably have better diets. As such, in this silly example they wouldn’t get lung cancer, and our experiment will fail, because it violates the structure of the “natural” world (the technical name for this is an “artifactual” result; see later).

One distinction worth making between two types of non-experimental research is the difference be- tween quasi-experimental research and case studies. The example I discussed earlier – in which we wanted to examine incidence of lung cancer among smokers and non-smokers, without trying to control who smokes and who doesn’t – is a quasi-experimental design. That is, it’s the same as an experiment, but we don’t control the predictors (IVs). We can still use statistics to analyse the results, it’s just that we have to be a lot more careful.

The alternative approach, case studies, aims to provide a very detailed description of one or a few instances. In general, you can’t use statistics to analyse the results of case studies, and it’s usually very hard to draw any general conclusions about “people in general” from a few isolated examples. However, case studies are very useful in some situations. Firstly, there are situations where you don’t have any alternative: neuropsychology has this issue a lot. Sometimes, you just can’t find a lot of people with brain damage in a specific area, so the only thing you can do is describe those cases that you do have in as much detail and with as much care as you can. However, there’s also some genuine advantages to case studies: because you don’t have as many people to study, you have the ability to invest lots of time and effort trying to understand the specific factors at play in each case. This is a very valuable thing to do. As a consequence, case studies can complement the more statistically-oriented approaches that you see in experimental and quasi-experimental designs. We won’t talk much about case studies in these lectures, but they are nevertheless very valuable tools!

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• Choosing the Right Statistical Test | Types & Examples

Choosing the Right Statistical Test | Types & Examples

Published on January 28, 2020 by Rebecca Bevans . Revised on June 22, 2023.

Statistical tests are used in hypothesis testing . They can be used to:

• determine whether a predictor variable has a statistically significant relationship with an outcome variable.
• estimate the difference between two or more groups.

Statistical tests assume a null hypothesis of no relationship or no difference between groups. Then they determine whether the observed data fall outside of the range of values predicted by the null hypothesis.

If you already know what types of variables you’re dealing with, you can use the flowchart to choose the right statistical test for your data.

Statistical tests flowchart

Table of contents

What does a statistical test do, when to perform a statistical test, choosing a parametric test: regression, comparison, or correlation, choosing a nonparametric test, flowchart: choosing a statistical test, other interesting articles, frequently asked questions about statistical tests.

Statistical tests work by calculating a test statistic – a number that describes how much the relationship between variables in your test differs from the null hypothesis of no relationship.

It then calculates a p value (probability value). The p -value estimates how likely it is that you would see the difference described by the test statistic if the null hypothesis of no relationship were true.

If the value of the test statistic is more extreme than the statistic calculated from the null hypothesis, then you can infer a statistically significant relationship between the predictor and outcome variables.

If the value of the test statistic is less extreme than the one calculated from the null hypothesis, then you can infer no statistically significant relationship between the predictor and outcome variables.

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You can perform statistical tests on data that have been collected in a statistically valid manner – either through an experiment , or through observations made using probability sampling methods .

For a statistical test to be valid , your sample size needs to be large enough to approximate the true distribution of the population being studied.

To determine which statistical test to use, you need to know:

• whether your data meets certain assumptions.
• the types of variables that you’re dealing with.

Statistical assumptions

Statistical tests make some common assumptions about the data they are testing:

• Independence of observations (a.k.a. no autocorrelation): The observations/variables you include in your test are not related (for example, multiple measurements of a single test subject are not independent, while measurements of multiple different test subjects are independent).
• Homogeneity of variance : the variance within each group being compared is similar among all groups. If one group has much more variation than others, it will limit the test’s effectiveness.
• Normality of data : the data follows a normal distribution (a.k.a. a bell curve). This assumption applies only to quantitative data .

If your data do not meet the assumptions of normality or homogeneity of variance, you may be able to perform a nonparametric statistical test , which allows you to make comparisons without any assumptions about the data distribution.

If your data do not meet the assumption of independence of observations, you may be able to use a test that accounts for structure in your data (repeated-measures tests or tests that include blocking variables).

Types of variables

The types of variables you have usually determine what type of statistical test you can use.

Quantitative variables represent amounts of things (e.g. the number of trees in a forest). Types of quantitative variables include:

• Continuous (aka ratio variables): represent measures and can usually be divided into units smaller than one (e.g. 0.75 grams).
• Discrete (aka integer variables): represent counts and usually can’t be divided into units smaller than one (e.g. 1 tree).

Categorical variables represent groupings of things (e.g. the different tree species in a forest). Types of categorical variables include:

• Ordinal : represent data with an order (e.g. rankings).
• Nominal : represent group names (e.g. brands or species names).
• Binary : represent data with a yes/no or 1/0 outcome (e.g. win or lose).

Choose the test that fits the types of predictor and outcome variables you have collected (if you are doing an experiment , these are the independent and dependent variables ). Consult the tables below to see which test best matches your variables.

Parametric tests usually have stricter requirements than nonparametric tests, and are able to make stronger inferences from the data. They can only be conducted with data that adheres to the common assumptions of statistical tests.

The most common types of parametric test include regression tests, comparison tests, and correlation tests.

Regression tests

Regression tests look for cause-and-effect relationships . They can be used to estimate the effect of one or more continuous variables on another variable.

Comparison tests

Comparison tests look for differences among group means . They can be used to test the effect of a categorical variable on the mean value of some other characteristic.

T-tests are used when comparing the means of precisely two groups (e.g., the average heights of men and women). ANOVA and MANOVA tests are used when comparing the means of more than two groups (e.g., the average heights of children, teenagers, and adults).

Correlation tests

Correlation tests check whether variables are related without hypothesizing a cause-and-effect relationship.

These can be used to test whether two variables you want to use in (for example) a multiple regression test are autocorrelated.

Non-parametric tests don’t make as many assumptions about the data, and are useful when one or more of the common statistical assumptions are violated. However, the inferences they make aren’t as strong as with parametric tests.

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This flowchart helps you choose among parametric tests. For nonparametric alternatives, check the table above.

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.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient
• Null hypothesis

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

Statistical tests commonly assume that:

• the data are normally distributed
• the groups that are being compared have similar variance
• the data are independent

If your data does not meet these assumptions you might still be able to use a nonparametric statistical test , which have fewer requirements but also make weaker inferences.

A test statistic is a number calculated by a  statistical test . It describes how far your observed data is from the  null hypothesis  of no relationship between  variables or no difference among sample groups.

The test statistic tells you how different two or more groups are from the overall population mean , or how different a linear slope is from the slope predicted by a null hypothesis . Different test statistics are used in different statistical tests.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g. the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g. water volume or weight).

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Study/Experimental/Research Design: Much More Than Statistics

Kenneth l. knight.

Brigham Young University, Provo, UT

The purpose of study, experimental, or research design in scientific manuscripts has changed significantly over the years. It has evolved from an explanation of the design of the experiment (ie, data gathering or acquisition) to an explanation of the statistical analysis. This practice makes “Methods” sections hard to read and understand.

To clarify the difference between study design and statistical analysis, to show the advantages of a properly written study design on article comprehension, and to encourage authors to correctly describe study designs.

Description:

The role of study design is explored from the introduction of the concept by Fisher through modern-day scientists and the AMA Manual of Style . At one time, when experiments were simpler, the study design and statistical design were identical or very similar. With the complex research that is common today, which often includes manipulating variables to create new variables and the multiple (and different) analyses of a single data set, data collection is very different than statistical design. Thus, both a study design and a statistical design are necessary.

Advantages:

Scientific manuscripts will be much easier to read and comprehend. A proper experimental design serves as a road map to the study methods, helping readers to understand more clearly how the data were obtained and, therefore, assisting them in properly analyzing the results.

Study, experimental, or research design is the backbone of good research. It directs the experiment by orchestrating data collection, defines the statistical analysis of the resultant data, and guides the interpretation of the results. When properly described in the written report of the experiment, it serves as a road map to readers, 1 helping them negotiate the “Methods” section, and, thus, it improves the clarity of communication between authors and readers.

A growing trend is to equate study design with only the statistical analysis of the data. The design statement typically is placed at the end of the “Methods” section as a subsection called “Experimental Design” or as part of a subsection called “Data Analysis.” This placement, however, equates experimental design and statistical analysis, minimizing the effect of experimental design on the planning and reporting of an experiment. This linkage is inappropriate, because some of the elements of the study design that should be described at the beginning of the “Methods” section are instead placed in the “Statistical Analysis” section or, worse, are absent from the manuscript entirely.

Have you ever interrupted your reading of the “Methods” to sketch out the variables in the margins of the paper as you attempt to understand how they all fit together? Or have you jumped back and forth from the early paragraphs of the “Methods” section to the “Statistics” section to try to understand which variables were collected and when? These efforts would be unnecessary if a road map at the beginning of the “Methods” section outlined how the independent variables were related, which dependent variables were measured, and when they were measured. When they were measured is especially important if the variables used in the statistical analysis were a subset of the measured variables or were computed from measured variables (such as change scores).

The purpose of this Communications article is to clarify the purpose and placement of study design elements in an experimental manuscript. Adopting these ideas may improve your science and surely will enhance the communication of that science. These ideas will make experimental manuscripts easier to read and understand and, therefore, will allow them to become part of readers' clinical decision making.

WHAT IS A STUDY (OR EXPERIMENTAL OR RESEARCH) DESIGN?

The terms study design, experimental design, and research design are often thought to be synonymous and are sometimes used interchangeably in a single paper. Avoid doing so. Use the term that is preferred by the style manual of the journal for which you are writing. Study design is the preferred term in the AMA Manual of Style , 2 so I will use it here.

A study design is the architecture of an experimental study 3 and a description of how the study was conducted, 4 including all elements of how the data were obtained. 5 The study design should be the first subsection of the “Methods” section in an experimental manuscript (see the Table ). “Statistical Design” or, preferably, “Statistical Analysis” or “Data Analysis” should be the last subsection of the “Methods” section.

Table. Elements of a “Methods” Section

The “Study Design” subsection describes how the variables and participants interacted. It begins with a general statement of how the study was conducted (eg, crossover trials, parallel, or observational study). 2 The second element, which usually begins with the second sentence, details the number of independent variables or factors, the levels of each variable, and their names. A shorthand way of doing so is with a statement such as “A 2 × 4 × 8 factorial guided data collection.” This tells us that there were 3 independent variables (factors), with 2 levels of the first factor, 4 levels of the second factor, and 8 levels of the third factor. Following is a sentence that names the levels of each factor: for example, “The independent variables were sex (male or female), training program (eg, walking, running, weight lifting, or plyometrics), and time (2, 4, 6, 8, 10, 15, 20, or 30 weeks).” Such an approach clearly outlines for readers how the various procedures fit into the overall structure and, therefore, enhances their understanding of how the data were collected. Thus, the design statement is a road map of the methods.

The dependent (or measurement or outcome) variables are then named. Details of how they were measured are not given at this point in the manuscript but are explained later in the “Instruments” and “Procedures” subsections.

Next is a paragraph detailing who the participants were and how they were selected, placed into groups, and assigned to a particular treatment order, if the experiment was a repeated-measures design. And although not a part of the design per se, a statement about obtaining written informed consent from participants and institutional review board approval is usually included in this subsection.

The nuts and bolts of the “Methods” section follow, including such things as equipment, materials, protocols, etc. These are beyond the scope of this commentary, however, and so will not be discussed.

The last part of the “Methods” section and last part of the “Study Design” section is the “Data Analysis” subsection. It begins with an explanation of any data manipulation, such as how data were combined or how new variables (eg, ratios or differences between collected variables) were calculated. Next, readers are told of the statistical measures used to analyze the data, such as a mixed 2 × 4 × 8 analysis of variance (ANOVA) with 2 between-groups factors (sex and training program) and 1 within-groups factor (time of measurement). Researchers should state and reference the statistical package and procedure(s) within the package used to compute the statistics. (Various statistical packages perform analyses slightly differently, so it is important to know the package and specific procedure used.) This detail allows readers to judge the appropriateness of the statistical measures and the conclusions drawn from the data.

STATISTICAL DESIGN VERSUS STATISTICAL ANALYSIS

Avoid using the term statistical design . Statistical methods are only part of the overall design. The term gives too much emphasis to the statistics, which are important, but only one of many tools used in interpreting data and only part of the study design:

The most important issues in biostatistics are not expressed with statistical procedures. The issues are inherently scientific, rather than purely statistical, and relate to the architectural design of the research, not the numbers with which the data are cited and interpreted. 6

Stated another way, “The justification for the analysis lies not in the data collected but in the manner in which the data were collected.” 3 “Without the solid foundation of a good design, the edifice of statistical analysis is unsafe.” 7 (pp4–5)

The intertwining of study design and statistical analysis may have been caused (unintentionally) by R.A. Fisher, “… a genius who almost single-handedly created the foundations for modern statistical science.” 8 Most research did not involve statistics until Fisher invented the concepts and procedures of ANOVA (in 1921) 9 , 10 and experimental design (in 1935). 11 His books became standard references for scientists in many disciplines. As a result, many ANOVA books were titled Experimental Design (see, for example, Edwards 12 ), and ANOVA courses taught in psychology and education departments included the words experimental design in their course titles.

Before the widespread use of computers to analyze data, designs were much simpler, and often there was little difference between study design and statistical analysis. So combining the 2 elements did not cause serious problems. This is no longer true, however, for 3 reasons: (1) Research studies are becoming more complex, with multiple independent and dependent variables. The procedures sections of these complex studies can be difficult to understand if your only reference point is the statistical analysis and design. (2) Dependent variables are frequently measured at different times. (3) How the data were collected is often not directly correlated with the statistical design.

For example, assume the goal is to determine the strength gain in novice and experienced athletes as a result of 3 strength training programs. Rate of change in strength is not a measurable variable; rather, it is calculated from strength measurements taken at various time intervals during the training. So the study design would be a 2 × 2 × 3 factorial with independent variables of time (pretest or posttest), experience (novice or advanced), and training (isokinetic, isotonic, or isometric) and a dependent variable of strength. The statistical design , however, would be a 2 × 3 factorial with independent variables of experience (novice or advanced) and training (isokinetic, isotonic, or isometric) and a dependent variable of strength gain. Note that data were collected according to a 3-factor design but were analyzed according to a 2-factor design and that the dependent variables were different. So a single design statement, usually a statistical design statement, would not communicate which data were collected or how. Readers would be left to figure out on their own how the data were collected.

MULTIVARIATE RESEARCH AND THE NEED FOR STUDY DESIGNS

With the advent of electronic data gathering and computerized data handling and analysis, research projects have increased in complexity. Many projects involve multiple dependent variables measured at different times, and, therefore, multiple design statements may be needed for both data collection and statistical analysis. Consider, for example, a study of the effects of heat and cold on neural inhibition. The variables of H max and M max are measured 3 times each: before, immediately after, and 30 minutes after a 20-minute treatment with heat or cold. Muscle temperature might be measured each minute before, during, and after the treatment. Although the minute-by-minute data are important for graphing temperature fluctuations during the procedure, only 3 temperatures (time 0, time 20, and time 50) are used for statistical analysis. A single dependent variable H max :M max ratio is computed to illustrate neural inhibition. Again, a single statistical design statement would tell little about how the data were obtained. And in this example, separate design statements would be needed for temperature measurement and H max :M max measurements.

As stated earlier, drawing conclusions from the data depends more on how the data were measured than on how they were analyzed. 3 , 6 , 7 , 13 So a single study design statement (or multiple such statements) at the beginning of the “Methods” section acts as a road map to the study and, thus, increases scientists' and readers' comprehension of how the experiment was conducted (ie, how the data were collected). Appropriate study design statements also increase the accuracy of conclusions drawn from the study.

CONCLUSIONS

The goal of scientific writing, or any writing, for that matter, is to communicate information. Including 2 design statements or subsections in scientific papers—one to explain how the data were collected and another to explain how they were statistically analyzed—will improve the clarity of communication and bring praise from readers. To summarize:

• Purge from your thoughts and vocabulary the idea that experimental design and statistical design are synonymous.
• Study or experimental design plays a much broader role than simply defining and directing the statistical analysis of an experiment.
• A properly written study design serves as a road map to the “Methods” section of an experiment and, therefore, improves communication with the reader.
• Study design should include a description of the type of design used, each factor (and each level) involved in the experiment, and the time at which each measurement was made.
• Clarify when the variables involved in data collection and data analysis are different, such as when data analysis involves only a subset of a collected variable or a resultant variable from the mathematical manipulation of 2 or more collected variables.

Acknowledgments

Thanks to Thomas A. Cappaert, PhD, ATC, CSCS, CSE, for suggesting the link between R.A. Fisher and the melding of the concepts of research design and statistics.

Population vs Sample – A Deep Dive with Examples

When conducting statistical analysis, one of the first things you must determine is whether you are working with population data or sample data. Getting this right is crucial, as it affects how you collect, analyze, and interpret the data.

In this comprehensive guide, we’ll clarify the difference between these two fundamental concepts in statistics and when to use each one.

Population Data

A population in statistics refers to the entire group that you want to study or analyze. It consists of all subjects that have at least one characteristic in common.

For example, the population could be:

• All social media users in the United States
• All students enrolled at a particular university
• All video game players between ages 18-35

The key thing is that the population encompasses the full set of subjects you are interested in.

Some key attributes of a population are:

• It includes all members of a defined group
• There is no limit on the size (it can be infinite)
• Parameters are used to describe population attributes (e.g. mean, standard deviation)

Parameters refer to summary statistics calculated for the entire population. Since you rarely have access to full population data, these are typically estimates.

Collecting Population Data

For small, well-defined populations, it may be feasible to gather data on every member. This is known as a census.

For example, a university may survey all 2000 enrolled students about their housing preferences. Or a company with 250 employees may poll everyone about benefits satisfaction.

For large, undefined groups however, surveying the entire population is nearly impossible. There are simply too many people spread across too large a geography.

Imagine trying to collect brand preference data from every single consumer in North America – not feasible!

This is why national statistical agencies like the US Census Bureau conduct censuses only every 10 years. Even then, some individuals inevitably get missed.

When to Use Population Data

Since population data is so difficult to obtain, it is rarely used in statistical analysis. Exceptions are when:

• The population is relatively small and accessible
• You have an urgent need for completely accurate data
• You have ample time and resources to survey an entire group

Government agencies and policy think tanks may undertake large population surveys to inform public services, infrastructure, health initiatives, etc.

Businesses typically don‘t deal with full population data given customer sets can be massive or undefined. Further, 100% accuracy usually isn‘t needed for commercial decisions.

Sample Data

A sample represents a subset of the larger population that you want to study. Sampling just a portion of the total population allows you to save significant time and resources.

The key benefit is that you can gather actionable insights without needing to collect data from every single member of the group.

Examples of samples could include:

• 500 social media users in the US
• 300 students at a university
• 150 video game players aged 18-35

Characteristics of Good Sample Data

While sampling reduces effort, you must ensure your sample provides an accurate reflection of the total population. Two key requirements are that the sample is:

• Randomly selected
• Sufficiently large

Random Selection

Each member of the population should have an equal, non-zero chance of being selected. No groups or individuals should be unfairly excluded.

Random sampling removes selection bias and allows you to achieve valid, reliable results. Simple random sampling is the most basic method, while stratified sampling divides the population into homogeneous subgroups first before sampling.

Sample Size

How big does your sample need to be? This depends on factors like:

• Population size – larger populations need bigger samples
• Acceptable error margin – higher precision requires larger samples
• Population variation – more diverse populations need bigger samples to capture variances
• Available resources – higher budgets allow larger samples

As a rule of thumb, a sample size of 100 is considered the minimum for drawing statistical conclusions. Many researchers recommend at least 300 – 500 subjects when possible.

You can use formulas to calculate minimum sample size, factoring in elements like margin of error and confidence level. Online sample size calculators are also available.

When to Use a Sample

For statistical analysis focused on real-world topics, sampling is vastly more common than using total population data given the latter is rarely accessible or practical at scale.

Sampling should be leveraged when:

• The target population is very large or unknown in exact size
• There is no way to practically reach or collect data from every member
• Time, access, budget, or other resources don’t allow a census
• 100% accuracy isn’t an absolute necessity

This covers the majority of statistical analysis done for research papers, political polls, clinical trials, market research, quality assurance sampling, and more.

You gain significant efficiency without sacrificing too much precision. The key is to sample thoughtfully!

Sampling Bias

While sampling saves time and effort, it introduces the risk of bias. Sampling bias occurs when the selection process systematically favors certain members of the population over others.

This skews the data and reduces accuracy. For example:

• Conducting an election poll by only calling landline phones would bias the results in favor of older voters
• Surveying shoppers at Whole Foods about their grocery budgets would bias the data towards higher-income households

Avoiding Sampling Bias

To avoid sampling bias:

• Clearly define the target population at the start
• Use random sampling methods rather than convenience sampling
• Employ stratification techniques if subgroup representation is needed
• Check that the characteristics of your final sample align with the overall population based on benchmark data
• Increase sample size wherever possible to dilute potential biases

With proper techniques, sampling lets you efficiently gather quality data that powerfully represents an entire target group.

Key Takeaways

• A population comprises all members of a defined group you want to study
• A sample is a segment of the population used to represent characteristics of the whole group
• Populations are often too large and inaccessible to survey completely
• Well-designed random sampling allows for efficient yet accurate data collection
• Avoid sampling bias through thoughtful selection and stratification approaches

Understanding these core concepts will vastly improve your statistical competency. For more guidance, explore online courses or reference books focused on data science and analytics.

Now get out there, sample thoughtfully, and uncover game-changing insights about your populations of interest!

Dr. Alex Mitchell is a dedicated coding instructor with a deep passion for teaching and a wealth of experience in computer science education. As a university professor, Dr. Mitchell has played a pivotal role in shaping the coding skills of countless students, helping them navigate the intricate world of programming languages and software development.

Beyond the classroom, Dr. Mitchell is an active contributor to the freeCodeCamp community, where he regularly shares his expertise through tutorials, code examples, and practical insights. His teaching repertoire includes a wide range of languages and frameworks, such as Python, JavaScript, Next.js, and React, which he presents in an accessible and engaging manner.

Dr. Mitchell’s approach to teaching blends academic rigor with real-world applications, ensuring that his students not only understand the theory but also how to apply it effectively. His commitment to education and his ability to simplify complex topics have made him a respected figure in both the university and online learning communities.

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