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Random Assignment in Experiments

By Jim Frost 4 Comments

Random assignment uses chance to assign subjects to the control and treatment groups in an experiment. This process helps ensure that the groups are equivalent at the beginning of the study, which makes it safer to assume the treatments caused any differences between groups that the experimenters observe at the end of the study.

Huh? That might be a big surprise! At this point, you might be wondering about all of those studies that use statistics to assess the effects of different treatments. There’s a critical separation between significance and causality:

• Statistical procedures determine whether an effect is significant.
• Experimental designs determine how confidently you can assume that a treatment causes the effect.

In this post, learn how using random assignment in experiments can help you identify causal relationships.

Correlation, Causation, and Confounding Variables

Random assignment helps you separate causation from correlation and rule out confounding variables. As a critical component of the scientific method , experiments typically set up contrasts between a control group and one or more treatment groups. The idea is to determine whether the effect, which is the difference between a treatment group and the control group, is statistically significant. If the effect is significant, group assignment correlates with different outcomes.

However, as you have no doubt heard, correlation does not necessarily imply causation. In other words, the experimental groups can have different mean outcomes, but the treatment might not be causing those differences even though the differences are statistically significant.

The difficulty in definitively stating that a treatment caused the difference is due to potential confounding variables or confounders. Confounders are alternative explanations for differences between the experimental groups. Confounding variables correlate with both the experimental groups and the outcome variable. In this situation, confounding variables can be the actual cause for the outcome differences rather than the treatments themselves. As you’ll see, if an experiment does not account for confounding variables, they can bias the results and make them untrustworthy.

Related posts : Understanding Correlation in Statistics , Causation versus Correlation , and Hill’s Criteria for Causation .

Example of Confounding in an Experiment

• Control group: Does not consume vitamin supplements
• Treatment group: Regularly consumes vitamin supplements.

Imagine we measure a specific health outcome. After the experiment is complete, we perform a 2-sample t-test to determine whether the mean outcomes for these two groups are different. Assume the test results indicate that the mean health outcome in the treatment group is significantly better than the control group.

Why can’t we assume that the vitamins improved the health outcomes? After all, only the treatment group took the vitamins.

Related post : Confounding Variables in Regression Analysis

Alternative Explanations for Differences in Outcomes

The answer to that question depends on how we assigned the subjects to the experimental groups. If we let the subjects decide which group to join based on their existing vitamin habits, it opens the door to confounding variables. It’s reasonable to assume that people who take vitamins regularly also tend to have other healthy habits. These habits are confounders because they correlate with both vitamin consumption (experimental group) and the health outcome measure.

Random assignment prevents this self sorting of participants and reduces the likelihood that the groups start with systematic differences.

In fact, studies have found that supplement users are more physically active, have healthier diets, have lower blood pressure, and so on compared to those who don’t take supplements. If subjects who already take vitamins regularly join the treatment group voluntarily, they bring these healthy habits disproportionately to the treatment group. Consequently, these habits will be much more prevalent in the treatment group than the control group.

The healthy habits are the confounding variables—the potential alternative explanations for the difference in our study’s health outcome. It’s entirely possible that these systematic differences between groups at the start of the study might cause the difference in the health outcome at the end of the study—and not the vitamin consumption itself!

If our experiment doesn’t account for these confounding variables, we can’t trust the results. While we obtained statistically significant results with the 2-sample t-test for health outcomes, we don’t know for sure whether the vitamins, the systematic difference in habits, or some combination of the two caused the improvements.

Learn why many randomized clinical experiments use a placebo to control for the Placebo Effect .

Experiments Must Account for Confounding Variables

Your experimental design must account for confounding variables to avoid their problems. Scientific studies commonly use the following methods to handle confounders:

• Use control variables to keep them constant throughout an experiment.
• Statistically control for them in an observational study.
• Use random assignment to reduce the likelihood that systematic differences exist between experimental groups when the study begins.

Let’s take a look at how random assignment works in an experimental design.

Random Assignment Can Reduce the Impact of Confounding Variables

Note that random assignment is different than random sampling. Random sampling is a process for obtaining a sample that accurately represents a population .

Random assignment uses a chance process to assign subjects to experimental groups. Using random assignment requires that the experimenters can control the group assignment for all study subjects. For our study, we must be able to assign our participants to either the control group or the supplement group. Clearly, if we don’t have the ability to assign subjects to the groups, we can’t use random assignment!

Additionally, the process must have an equal probability of assigning a subject to any of the groups. For example, in our vitamin supplement study, we can use a coin toss to assign each subject to either the control group or supplement group. For more complex experimental designs, we can use a random number generator or even draw names out of a hat.

Random Assignment Distributes Confounders Equally

The random assignment process distributes confounding properties amongst your experimental groups equally. In other words, randomness helps eliminate systematic differences between groups. For our study, flipping the coin tends to equalize the distribution of subjects with healthier habits between the control and treatment group. Consequently, these two groups should start roughly equal for all confounding variables, including healthy habits!

Random assignment is a simple, elegant solution to a complex problem. For any given study area, there can be a long list of confounding variables that you could worry about. However, using random assignment, you don’t need to know what they are, how to detect them, or even measure them. Instead, use random assignment to equalize them across your experimental groups so they’re not a problem.

Because random assignment helps ensure that the groups are comparable when the experiment begins, you can be more confident that the treatments caused the post-study differences. Random assignment helps increase the internal validity of your study.

Comparing the Vitamin Study With and Without Random Assignment

Let’s compare two scenarios involving our hypothetical vitamin study. We’ll assume that the study obtains statistically significant results in both cases.

Scenario 1: We don’t use random assignment and, unbeknownst to us, subjects with healthier habits disproportionately end up in the supplement treatment group. The experimental groups differ by both healthy habits and vitamin consumption. Consequently, we can’t determine whether it was the habits or vitamins that improved the outcomes.

Scenario 2: We use random assignment and, consequently, the treatment and control groups start with roughly equal levels of healthy habits. The intentional introduction of vitamin supplements in the treatment group is the primary difference between the groups. Consequently, we can more confidently assert that the supplements caused an improvement in health outcomes.

For both scenarios, the statistical results could be identical. However, the methodology behind the second scenario makes a stronger case for a causal relationship between vitamin supplement consumption and health outcomes.

How important is it to use the correct methodology? Well, if the relationship between vitamins and health outcomes is not causal, then consuming vitamins won’t cause your health outcomes to improve regardless of what the study indicates. Instead, it’s probably all the other healthy habits!

Learn more about Randomized Controlled Trials (RCTs) that are the gold standard for identifying causal relationships because they use random assignment.

Drawbacks of Random Assignment

Random assignment helps reduce the chances of systematic differences between the groups at the start of an experiment and, thereby, mitigates the threats of confounding variables and alternative explanations. However, the process does not always equalize all of the confounding variables. Its random nature tends to eliminate systematic differences, but it doesn’t always succeed.

Sometimes random assignment is impossible because the experimenters cannot control the treatment or independent variable. For example, if you want to determine how individuals with and without depression perform on a test, you cannot randomly assign subjects to these groups. The same difficulty occurs when you’re studying differences between genders.

In other cases, there might be ethical issues. For example, in a randomized experiment, the researchers would want to withhold treatment for the control group. However, if the treatments are vaccinations, it might be unethical to withhold the vaccinations.

Other times, random assignment might be possible, but it is very challenging. For example, with vitamin consumption, it’s generally thought that if vitamin supplements cause health improvements, it’s only after very long-term use. It’s hard to enforce random assignment with a strict regimen for usage in one group and non-usage in the other group over the long-run. Or imagine a study about smoking. The researchers would find it difficult to assign subjects to the smoking and non-smoking groups randomly!

Fortunately, if you can’t use random assignment to help reduce the problem of confounding variables, there are different methods available. The other primary approach is to perform an observational study and incorporate the confounders into the statistical model itself. For more information, read my post Observational Studies Explained .

Read About Real Experiments that Used Random Assignment

I’ve written several blog posts about studies that have used random assignment to make causal inferences. Read studies about the following:

• Flu Vaccinations
• COVID-19 Vaccinations

Sullivan L.  Random assignment versus random selection . SAGE Glossary of the Social and Behavioral Sciences, SAGE Publications, Inc.; 2009.

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Reader Interactions

November 13, 2019 at 4:59 am

Hi Jim, I have a question of randomly assigning participants to one of two conditions when it is an ongoing study and you are not sure of how many participants there will be. I am using this random assignment tool for factorial experiments. http://methodologymedia.psu.edu/most/rannumgenerator It asks you for the total number of participants but at this point, I am not sure how many there will be. Thanks for any advice you can give me, Floyd

May 28, 2019 at 11:34 am

Jim, can you comment on the validity of using the following approach when we can’t use random assignments. I’m in education, we have an ACT prep course that we offer. We can’t force students to take it and we can’t keep them from taking it either. But we want to know if it’s working. Let’s say that by senior year all students who are going to take the ACT have taken it. Let’s also say that I’m only including students who have taking it twice (so I can show growth between first and second time taking it). What I’ve done to address confounders is to go back to say 8th or 9th grade (prior to anyone taking the ACT or the ACT prep course) and run an analysis showing the two groups are not significantly different to start with. Is this valid? If the ACT prep students were higher achievers in 8th or 9th grade, I could not assume my prep course is effecting greater growth, but if they were not significantly different in 8th or 9th grade, I can assume the significant difference in ACT growth (from first to second testing) is due to the prep course. Yes or no?

May 26, 2019 at 5:37 pm

Nice post! I think the key to understanding scientific research is to understand randomization. And most people don’t get it.

May 27, 2019 at 9:48 pm

Thank you, Anoop!

I think randomness in an experiment is a funny thing. The issue of confounding factors is a serious problem. You might not even know what they are! But, use random assignment and, voila, the problem usually goes away! If you can’t use random assignment, suddenly you have a whole host of issues to worry about, which I’ll be writing about in more detail in my upcoming post about observational experiments!

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Methodology

• Random Assignment in Experiments | Introduction & Examples

Random Assignment in Experiments | Introduction & Examples

Published on March 8, 2021 by Pritha Bhandari . Revised on June 22, 2023.

In experimental research, random assignment is a way of placing participants from your sample into different treatment groups using randomization.

With simple random assignment, every member of the sample has a known or equal chance of being placed in a control group or an experimental group. Studies that use simple random assignment are also called completely randomized designs .

Random assignment is a key part of experimental design . It helps you ensure that all groups are comparable at the start of a study: any differences between them are due to random factors, not research biases like sampling bias or selection bias .

Table of contents

Why does random assignment matter, random sampling vs random assignment, how do you use random assignment, when is random assignment not used, other interesting articles, frequently asked questions about random assignment.

Random assignment is an important part of control in experimental research, because it helps strengthen the internal validity of an experiment and avoid biases.

In experiments, researchers manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. To do so, they often use different levels of an independent variable for different groups of participants.

This is called a between-groups or independent measures design.

You use three groups of participants that are each given a different level of the independent variable:

• a control group that’s given a placebo (no dosage, to control for a placebo effect ),
• an experimental group that’s given a low dosage,
• a second experimental group that’s given a high dosage.

Random assignment to helps you make sure that the treatment groups don’t differ in systematic ways at the start of the experiment, as this can seriously affect (and even invalidate) your work.

If you don’t use random assignment, you may not be able to rule out alternative explanations for your results.

• participants recruited from cafes are placed in the control group ,
• participants recruited from local community centers are placed in the low dosage experimental group,
• participants recruited from gyms are placed in the high dosage group.

With this type of assignment, it’s hard to tell whether the participant characteristics are the same across all groups at the start of the study. Gym-users may tend to engage in more healthy behaviors than people who frequent cafes or community centers, and this would introduce a healthy user bias in your study.

Although random assignment helps even out baseline differences between groups, it doesn’t always make them completely equivalent. There may still be extraneous variables that differ between groups, and there will always be some group differences that arise from chance.

Most of the time, the random variation between groups is low, and, therefore, it’s acceptable for further analysis. This is especially true when you have a large sample. In general, you should always use random assignment in experiments when it is ethically possible and makes sense for your study topic.

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Random sampling and random assignment are both important concepts in research, but it’s important to understand the difference between them.

Random sampling (also called probability sampling or random selection) is a way of selecting members of a population to be included in your study. In contrast, random assignment is a way of sorting the sample participants into control and experimental groups.

While random sampling is used in many types of studies, random assignment is only used in between-subjects experimental designs.

Some studies use both random sampling and random assignment, while others use only one or the other.

Random sampling enhances the external validity or generalizability of your results, because it helps ensure that your sample is unbiased and representative of the whole population. This allows you to make stronger statistical inferences .

You use a simple random sample to collect data. Because you have access to the whole population (all employees), you can assign all 8000 employees a number and use a random number generator to select 300 employees. These 300 employees are your full sample.

Random assignment enhances the internal validity of the study, because it ensures that there are no systematic differences between the participants in each group. This helps you conclude that the outcomes can be attributed to the independent variable .

• a control group that receives no intervention.
• an experimental group that has a remote team-building intervention every week for a month.

You use random assignment to place participants into the control or experimental group. To do so, you take your list of participants and assign each participant a number. Again, you use a random number generator to place each participant in one of the two groups.

To use simple random assignment, you start by giving every member of the sample a unique number. Then, you can use computer programs or manual methods to randomly assign each participant to a group.

• Random number generator: Use a computer program to generate random numbers from the list for each group.
• Lottery method: Place all numbers individually in a hat or a bucket, and draw numbers at random for each group.
• Flip a coin: When you only have two groups, for each number on the list, flip a coin to decide if they’ll be in the control or the experimental group.
• Use a dice: When you have three groups, for each number on the list, roll a dice to decide which of the groups they will be in. For example, assume that rolling 1 or 2 lands them in a control group; 3 or 4 in an experimental group; and 5 or 6 in a second control or experimental group.

This type of random assignment is the most powerful method of placing participants in conditions, because each individual has an equal chance of being placed in any one of your treatment groups.

Random assignment in block designs

In more complicated experimental designs, random assignment is only used after participants are grouped into blocks based on some characteristic (e.g., test score or demographic variable). These groupings mean that you need a larger sample to achieve high statistical power .

For example, a randomized block design involves placing participants into blocks based on a shared characteristic (e.g., college students versus graduates), and then using random assignment within each block to assign participants to every treatment condition. This helps you assess whether the characteristic affects the outcomes of your treatment.

In an experimental matched design , you use blocking and then match up individual participants from each block based on specific characteristics. Within each matched pair or group, you randomly assign each participant to one of the conditions in the experiment and compare their outcomes.

Sometimes, it’s not relevant or ethical to use simple random assignment, so groups are assigned in a different way.

When comparing different groups

Sometimes, differences between participants are the main focus of a study, for example, when comparing men and women or people with and without health conditions. Participants are not randomly assigned to different groups, but instead assigned based on their characteristics.

In this type of study, the characteristic of interest (e.g., gender) is an independent variable, and the groups differ based on the different levels (e.g., men, women, etc.). All participants are tested the same way, and then their group-level outcomes are compared.

When it’s not ethically permissible

When studying unhealthy or dangerous behaviors, it’s not possible to use random assignment. For example, if you’re studying heavy drinkers and social drinkers, it’s unethical to randomly assign participants to one of the two groups and ask them to drink large amounts of alcohol for your experiment.

When you can’t assign participants to groups, you can also conduct a quasi-experimental study . In a quasi-experiment, you study the outcomes of pre-existing groups who receive treatments that you may not have any control over (e.g., heavy drinkers and social drinkers). These groups aren’t randomly assigned, but may be considered comparable when some other variables (e.g., age or socioeconomic status) are controlled for.

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

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Quartiles & Quantiles
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Prospective cohort study

Research bias

• Implicit bias
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic
• Social desirability bias

In experimental research, random assignment is a way of placing participants from your sample into different groups using randomization. With this method, every member of the sample has a known or equal chance of being placed in a control group or an experimental group.

Random selection, or random sampling , is a way of selecting members of a population for your study’s sample.

In contrast, random assignment is a way of sorting the sample into control and experimental groups.

Random sampling enhances the external validity or generalizability of your results, while random assignment improves the internal validity of your study.

Random assignment is used in experiments with a between-groups or independent measures design. In this research design, there’s usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable.

In general, you should always use random assignment in this type of experimental design when it is ethically possible and makes sense for your study topic.

To implement random assignment , assign a unique number to every member of your study’s sample .

Then, you can use a random number generator or a lottery method to randomly assign each number to a control or experimental group. You can also do so manually, by flipping a coin or rolling a dice to randomly assign participants to groups.

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Random Assignment

Random assignment refers to assigning participants or subjects into different groups (e.g., control group vs. treatment group) randomly. This helps ensure that any differences observed between groups are due to treatment effects rather than pre-existing differences.

Related terms

Experimental Design : Experimental design involves planning and structuring an experiment to minimize bias and maximize the ability to draw valid conclusions.

Control Group : A control group is a group that does not receive the experimental treatment and serves as a baseline for comparison.

Treatment Group : A treatment group is a group that receives the experimental treatment or intervention being studied.

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Study guides ( 4 ).

• AP Statistics - 3.1 Introducing Statistics: Do the Data We Collected Tell the Truth?
• AP Statistics - 3.2 Introduction to Planning a Study
• AP Statistics - 3.5 Introduction to Experimental Design
• AP Statistics - 3.7 Inference and Experiments

Subjects ( 5 )

• AP Psychology
• Abnormal Psychology
• College Introductory Statistics
• Honors Statistics
• Intro to Business Statistics

Practice Questions ( 2 )

• What is random assignment in experimental research design?
• What does random assignment allow researchers to conclude about observed changes?

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What’s Covered:

• How Will AP Scores Impact Your College Chances?
• Overview of the AP Stats Exam
• Hard AP Stats Questions

Whether you’ve taken an AP exam or not, you’ve likely heard about their notorious rigor and difficulty. After all, these exams are meant to evaluate whether you have a college-level grasp of the material.

AP Statistics is one of the harder AP exams ; in 2020, the AP Statistics Exam had a pass rate of 60%, with 16.2% of test-takers receiving a score of 5. Keep reading to learn more about the AP Statistics exam and see some harder problems—with detailed explanations!

How Will AP Scores Impact My College Chances?

AP scores alone generally don’t impact your college chances much. In fact, most colleges don’t require you to report your score, though self-reporting is optional. Taking AP classes in general, however, is beneficial to your college chances since they’re important in demonstrating to colleges your aptitude in a particular subject. To learn how your course rigor impacts your chances, we recommend using our free Admissions Chances calculator , which will let you know your odds of getting into hundreds of schools!

But, this doesn’t mean your scores aren’t important–some colleges will waive course requirements if your score is high enough. Though the requirements vary from school to school, it’s generally in your best interest to aim for a high score on your AP exams. Read more about the effect of AP Scores on your college chances .

Overview of the AP Statistics Exam

For the 2021 testing year, CollegeBoard is offering three different administrations of the AP Statistics exam . The first two administrations will be the traditional paper format, and the third administration will be digital.

The paper administration is held on May 17, 2021 and consists of two sections:

• Section I: 40 multiple choice questions (1 hour 30 minutes), 50% of exam score
• Section II: 6 free response questions (1 hour 30 minutes), 50% of exam score

The digital administration is held on May 25, 2021 and consists of two sections:

• Section II: 11 multiple choice questions (25 minutes) and 4 free response questions (1 hour 5 minutes), 50% of exam score

Regardless of which administration you take, the exam will test your knowledge of the following skill categories:

• Selecting statistical methods
• Data analysis
• Using probability and simulation
• Statistical argumentation 

You’ll also need a graphing calculator to take the exam, so make sure you’re comfortable using a graphing calculator to solve statistics problems.

10 Hardest AP Statistics Questions

Here are some sample AP Statistics questions which are on the tougher side.

Since this question deals with expected value, we’ll need the following given formula:

In this formula, \(E(x)\) (or \(\mu_x\) ) represents the expected value, and it’s equal to the sum of each event \((x_i)\) multiplied by the probability of that event \((p_i)\) .

With expected value problems, it’s usually best to construct a table.

First, recall that we want it to be advantageous to guess. This means the expected value of guessing should be higher than 2 (since leaving the question blank results in a score of 2).

So, if we are left with \(n\)  answer choices, we can construct the following table:

For a correct response, the x-value is 7 (since a score of 7 is given for each correct answer), and the probability is \(\frac{1}{n}\) (if there are \(n\)  answer choices, you have a 1 in \(n\) chance of guessing the correct answer). 

Similarly, for an incorrect response, the x-value is 0, and the probability is \(1-\frac{1}{n}\)  (since you can either get a question correct or incorrect). 

So, \(E(x)=7(1/n)+0(1-1/n)\gt 2\)

This simplifies to: \(7/n\gt 2\) , which means that \(n\lt 3.5\) . So, we would need 3 answer choices left for it to be advantageous to guess.

But, this question is tricky since it asks for the number of answer choices that should be eliminated, not left. Thus, we have \(5-3=2\) , and the correct answer is C.

Question 2 

Based on the information given, we can start by stating that  \(P(A)=0.01, P(B)=0.03,\) and \(P(C)=0.04.\)

Since any one component failing will cause the device to fail, the probability of the device failing is \(P(A) \bigcup P(B) \bigcup P(C)\) . So, the probability that the device will not fail is \(1-P(A) \bigcup P(B) \bigcup P(C)\) .

The AP Statistics Exam gives the following formula for calculating the union between two events:

So, in our case we have that: \(P(A) \bigcup P(B) \bigcup P(C)=P(A)+P(B)+P(C)-P(A\bigcap B\bigcap C)\) . 

To find \(P(A\bigcap B\bigcap C)\) , note that the problem stated that “the components fail independently of one another.” This means that \(P(A\bigcap B\bigcap C)=P(A)*P(B)*P(C)\) .

Then, \(P(A) \bigcup P(B) \bigcup P(C)=P(A)+P(B)+P(C)-P(A)*P(B)*P(C).\)

So, if we substitute the corresponding values, we get:

\(P(A) \bigcup P(B) \bigcup P(C)=0.01+0.03+0.04-(0.01*0.03*0.04)=0.79988.\)

This means our answer should be \(1-0.79988\approx 0.922\) , which corresponds to answer choice D.

You should definitely expect to be tested on inference, random sampling and random assignment on the AP Statistics exam. The general rule of thumb is:

If you have random sampling , you can generalize to the population.

If you have random assignment , you can conclude cause and effect.

For this question, it’s asking if we can assume that “the difference in sales was caused by the different cover designs.” So, we’re essentially being asked if we can draw conclusions about cause and effect. This means we need to check if the experiment had random assignment.

When describing the experiment, the question states that “thirty-five of these stores were randomly assigned,” so we do have random assignment! This means the correct answer is D, since random assignment allows us to draw an inference about the difference in sales being caused by cover design.

The AP Statistics Exam expects you to not only conduct different tests, but also understand when to use each type of test. With this question, we can start by eliminating D and E; since we are not given information about either population’s standard deviation, we will have to conduct a t -test instead of a z -test.

Next, since we’re determining whether Brand A batteries last longer than Brand B batteries, our test should be one-sided. Had the question asked if there was a difference between the two brands, we would then use a two-sided test, since we’d want to know if Brand A lasts longer or shorter than Brand B. So, we can also eliminate answer choice C.

Finally, we need to determine if a paired or two-sample test would be more appropriate. Because the question told us that the batteries were tested independently, it’s better to use a two-sample test. Thus, the best answer choice is B. 

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The power of a test is the probability of correctly rejecting the null hypothesis when it is false. This question gives us the alternative hypothesis (\(H_{a}: \mu \lt 10\) ), so if we reject the null hypothesis, this alternate hypothesis should be true. 

Because answer choices C, D, and E all render the alternative hypothesis false (since the actual means would be greater than 10), they’re incorrect. Answer choice A is correct because it would result in a greater power than B, since 8 is even farther from 10 than 9 is.

Along with the different types of tests, the AP Statistics Exam expects you to know the different sampling and survey methods. In this case, the bank is surveying all of its employees, so we have a census. For these questions, answering by elimination is a useful strategy.

Choice A is incorrect because though observational studies cannot determine cause and effect relationships, they can still give important correlative data. Choice B is incorrect since it contains the word “causes” (again, observational studies cannot prove cause and effect). Choice C is incorrect since, though there wasn’t a random sample, this does not mean no useful information can be gained. In fact, since the whole population was surveyed, there is a lot of useful information that can be gathered because no generalizations have to be made. 

Finally, choice D is incorrect since the entire population was surveyed, so there is no need to estimate the proportion of employees who participate in volunteer activities–the survey results will give an accurate proportion. This same reasoning is why answer choice E is correct.

Multiple-select questions such as these are notoriously difficult. However, if we consider each statement separately, we should be able to determine the correct answer fairly easily.

The first statement should be true. If the experiment finds that the drug had no effect, that means we cannot reject the null hypothesis. This occurs when the p-value is greater than 0.05.

The second statement is also true. If there was an unequal number of experiments positive and negative values of drug effect, the data would indicate that the drug did have an effect (since the number of positive values would outweigh the number of negative values, or vice versa).

Finally, the third statement is correct. If 0 is included in a confidence interval, this is equivalent to saying that no change has occurred (because the drug effect could be 0).

Since all three statements are true, the answer is E.

For this question, we’ll need to pay close attention to the labels on the table. The answer is choice A since it says that owning a car makes you more likely to live elsewhere than downtown. Let’s analyze the data:

Proportion of individuals who own a car that live in the downtown area: 10/60

Proportion of individuals who own a car that live elsewhere in the city: 15/60

The reason both fractions are out of 60 is that we are only looking at people who own a car (and there are 60 such employees). So, since 15/60 > 10/60, people who own cars are more likely to live elsewhere than downtown.

B is not correct because the proportion of people who don’t own a car and live outside the city (25/140) is greater than the proportion of people who don’t own a car and live in the city (115/140).

C is not correct because of the 60 people who own a car, more live outside the city (35) than in the city (25).

D is not correct because there is an equal number of people living in the downtown area of the city vs. elsewhere in the city.

E is incorrect because more people do not own a car (140) than those who do (60).

For this question, we’ll need to use the following given formula:

The margin of error is the part that includes the critical value multiplied by the standard deviation of the statistic.

To find the critical value, note that we have a 98% confidence interval. This means that the middle area is 98%, and thus the area to the left is 1%. The following diagram illustrates this:

So, to find the z-value, we can use the InvNorm function on the calculator, with an input of 0.01 (referring to the 1% on each side), to get that \(z=2.33\) .

Next, since we know the population proportion (79% of adults in the US use the internet), we can use the following formula to find the standard deviation of the statistic:

In this formula, \(\sigma _{\hat{p}}\) represents the standard deviation of the statistic, \(p\)  represents the proportion of the population (adults in the US) who use the internet, and \(n\) represents the sample size, which we are trying to find. 

Since \(p=0.79\) , our standard deviation is \(\sqrt{\frac{.79(1-.79)}{n}}\).

Then, the correct answer is either D or E. But, we were given that the margin of error should be less than 2.5%, so answer D is the correct choice.

Question 10

You might be tempted to analyze the possible outcomes to determine the most reasonable distribution and answer the question. While this method will certainly get you the right answer, a more simplified approach involves the process of elimination.

To start off, we can easily eliminate answer choices A, B, and E. This is because the difference between the red and green die can be a negative value.

Next, when choosing between C and D, note that with C, the middle values are more likely, and with D, all values are equally likely. But, let’s consider the outcomes 0 and 5.

For the outcome to be 0, we would need to have red – green be 0. This is possible when the red and green die show the same value, so we could have the following combinations:

Red: 1, Green: 1 

Red: 2, Green: 2

Red: 3, Green: 3

Red: 4, Green: 4

Red: 5, Green: 5

Red: 6, Green: 6

For the outcome to be 5, we would need to have red – green be 5. This is only possible when we have that:

Red: 6, Green: 1

So, we can clearly see that getting a result of 0 is much more likely than a result of 5, and C is the correct answer choice.

Here are some final tips to guide you as you’re studying for the AP Statistics Exam:

1. Use your calculator

As you complete practice problems and practice exams, make sure to practice using your calculator! In most cases, a calculator will simplify a problem or make it much quicker to answer. So, ensuring that you’re comfortable using your calculator will ease the test-taking process. Because both the multiple-choice and free-response portions of the AP Statistics Exam depend more heavily on a calculator than other AP exams, you’ll want to brush up on your calculator skills prior to taking the test.

2. Read carefully

Though this is a useful tip for any exam, it’s especially important for the AP Statistics test. Remember, these problems are designed to trick you, and there are often major details hidden in the fine print. Practice active reading by underling, circling, or boxing key terms, numbers or other information.

Also, reading carefully is especially important with graphics. Pay close attention to the labels on any charts, plots, or tables, as these will be key in determining the correct answer. 

Finally, here are some additional resources that might be helpful as you prepare for this exam:

• Ultimate Guide to the AP Stats Exam
• 2021 AP Exam Schedule + Study Tips
• How to Understand and Interpret Your AP Scores
• How Long Is Each AP Exam? A Complete List

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Random Assignment in Psychology: Definition & Examples

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In psychology, random assignment refers to the practice of allocating participants to different experimental groups in a study in a completely unbiased way, ensuring each participant has an equal chance of being assigned to any group.

In experimental research, random assignment, or random placement, organizes participants from your sample into different groups using randomization. 

Random assignment uses chance procedures to ensure that each participant has an equal opportunity of being assigned to either a control or experimental group.

The control group does not receive the treatment in question, whereas the experimental group does receive the treatment.

When using random assignment, neither the researcher nor the participant can choose the group to which the participant is assigned. This ensures that any differences between and within the groups are not systematic at the onset of the study. 

In a study to test the success of a weight-loss program, investigators randomly assigned a pool of participants to one of two groups.

Group A participants participated in the weight-loss program for 10 weeks and took a class where they learned about the benefits of healthy eating and exercise.

Group B participants read a 200-page book that explains the benefits of weight loss. The investigator randomly assigned participants to one of the two groups.

The researchers found that those who participated in the program and took the class were more likely to lose weight than those in the other group that received only the book.

Importance 

Random assignment ensures that each group in the experiment is identical before applying the independent variable.

In experiments , researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables. Random assignment increases the likelihood that the treatment groups are the same at the onset of a study.

Thus, any changes that result from the independent variable can be assumed to be a result of the treatment of interest. This is particularly important for eliminating sources of bias and strengthening the internal validity of an experiment.

Random assignment is the best method for inferring a causal relationship between a treatment and an outcome.

Random Selection vs. Random Assignment 

Random selection (also called probability sampling or random sampling) is a way of randomly selecting members of a population to be included in your study.

On the other hand, random assignment is a way of sorting the sample participants into control and treatment groups. 

Random selection ensures that everyone in the population has an equal chance of being selected for the study. Once the pool of participants has been chosen, experimenters use random assignment to assign participants into groups. 

Random assignment is only used in between-subjects experimental designs, while random selection can be used in a variety of study designs.

Random Assignment vs Random Sampling

Random sampling refers to selecting participants from a population so that each individual has an equal chance of being chosen. This method enhances the representativeness of the sample.

Random assignment, on the other hand, is used in experimental designs once participants are selected. It involves allocating these participants to different experimental groups or conditions randomly.

This helps ensure that any differences in results across groups are due to manipulating the independent variable, not preexisting differences among participants.

When to Use Random Assignment

Random assignment is used in experiments with a between-groups or independent measures design.

In these research designs, researchers will manipulate an independent variable to assess its effect on a dependent variable, while controlling for other variables.

There is usually a control group and one or more experimental groups. Random assignment helps ensure that the groups are comparable at the onset of the study.

How to Use Random Assignment

There are a variety of ways to assign participants into study groups randomly. Here are a handful of popular methods: 

• Random Number Generator : Give each member of the sample a unique number; use a computer program to randomly generate a number from the list for each group.
• Lottery : Give each member of the sample a unique number. Place all numbers in a hat or bucket and draw numbers at random for each group.
• Flipping a Coin : Flip a coin for each participant to decide if they will be in the control group or experimental group (this method can only be used when you have just two groups) 
• Roll a Die : For each number on the list, roll a dice to decide which of the groups they will be in. For example, assume that rolling 1, 2, or 3 places them in a control group and rolling 3, 4, 5 lands them in an experimental group.

When is Random Assignment not used?

• When it is not ethically permissible: Randomization is only ethical if the researcher has no evidence that one treatment is superior to the other or that one treatment might have harmful side effects. 
• When answering non-causal questions : If the researcher is just interested in predicting the probability of an event, the causal relationship between the variables is not important and observational designs would be more suitable than random assignment. 
• When studying the effect of variables that cannot be manipulated: Some risk factors cannot be manipulated and so it would not make any sense to study them in a randomized trial. For example, we cannot randomly assign participants into categories based on age, gender, or genetic factors.

Drawbacks of Random Assignment

While randomization assures an unbiased assignment of participants to groups, it does not guarantee the equality of these groups. There could still be extraneous variables that differ between groups or group differences that arise from chance. Additionally, there is still an element of luck with random assignments.

Thus, researchers can not produce perfectly equal groups for each specific study. Differences between the treatment group and control group might still exist, and the results of a randomized trial may sometimes be wrong, but this is absolutely okay.

Scientific evidence is a long and continuous process, and the groups will tend to be equal in the long run when data is aggregated in a meta-analysis.

Additionally, external validity (i.e., the extent to which the researcher can use the results of the study to generalize to the larger population) is compromised with random assignment.

Random assignment is challenging to implement outside of controlled laboratory conditions and might not represent what would happen in the real world at the population level. 

Random assignment can also be more costly than simple observational studies, where an investigator is just observing events without intervening with the population.

Randomization also can be time-consuming and challenging, especially when participants refuse to receive the assigned treatment or do not adhere to recommendations. 

What is the difference between random sampling and random assignment?

Random sampling refers to randomly selecting a sample of participants from a population. Random assignment refers to randomly assigning participants to treatment groups from the selected sample.

Does random assignment increase internal validity?

Yes, random assignment ensures that there are no systematic differences between the participants in each group, enhancing the study’s internal validity .

Does random assignment reduce sampling error?

Yes, with random assignment, participants have an equal chance of being assigned to either a control group or an experimental group, resulting in a sample that is, in theory, representative of the population.

Random assignment does not completely eliminate sampling error because a sample only approximates the population from which it is drawn. However, random sampling is a way to minimize sampling errors. 

When is random assignment not possible?

Random assignment is not possible when the experimenters cannot control the treatment or independent variable.

For example, if you want to compare how men and women perform on a test, you cannot randomly assign subjects to these groups.

Participants are not randomly assigned to different groups in this study, but instead assigned based on their characteristics.

Does random assignment eliminate confounding variables?

Yes, random assignment eliminates the influence of any confounding variables on the treatment because it distributes them at random among the study groups. Randomization invalidates any relationship between a confounding variable and the treatment.

Why is random assignment of participants to treatment conditions in an experiment used?

Random assignment is used to ensure that all groups are comparable at the start of a study. This allows researchers to conclude that the outcomes of the study can be attributed to the intervention at hand and to rule out alternative explanations for study results.

Further Reading

• Bogomolnaia, A., & Moulin, H. (2001). A new solution to the random assignment problem .  Journal of Economic theory ,  100 (2), 295-328.
• Krause, M. S., & Howard, K. I. (2003). What random assignment does and does not do .  Journal of Clinical Psychology ,  59 (7), 751-766.

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Unit 9: Sampling distributions

About this unit.

A sampling distribution shows every possible result a statistic can take in every possible sample from a population and how often each result happens - and can help us use samples to make predictions about the chance tht something will occur. This unit covers how sample proportions and sample means behave in repeated samples.

The normal distribution, revisited

• Density Curves (Opens a modal)
• Probabilities from density curves (Opens a modal)
• Probability in normal density curves Get 3 of 4 questions to level up!

The central limit theorem

• Introduction to sampling distributions (Opens a modal)
• Central limit theorem (Opens a modal)
• Sampling distribution of the sample mean (Opens a modal)
• Sampling distribution of the sample mean (part 2) (Opens a modal)
• Sample means and the central limit theorem Get 3 of 4 questions to level up!

Biased and unbiased point estimates

• Sample statistic bias worked example (Opens a modal)
• Biased and unbiased estimators Get 3 of 4 questions to level up!

Sampling distributions for sample proportions

• Sampling distribution of sample proportion part 1 (Opens a modal)
• Sampling distribution of sample proportion part 2 (Opens a modal)
• Normal conditions for sampling distributions of sample proportions (Opens a modal)
• Probability of sample proportions example (Opens a modal)
• Sampling distribution of a sample proportion example (Opens a modal)
• The normal condition for sample proportions Get 3 of 4 questions to level up!
• Mean and standard deviation of sample proportions Get 3 of 4 questions to level up!
• Finding probabilities with sample proportions Get 3 of 4 questions to level up!

Sampling distributions for differences in sample proportions

• Sampling distribution of the difference in sample proportions (Opens a modal)
• Sampling distribution of the difference in sample proportions: Probability example (Opens a modal)
• Differences of sample proportions — Probability examples (Opens a modal)
• Mean and standard deviation of difference of sample proportions Get 3 of 4 questions to level up!
• Shape of sampling distributions for differences in sample proportions Get 3 of 4 questions to level up!

Sampling distributions for sample means

• Standard error of the mean (Opens a modal)
• Example: Probability of sample mean exceeding a value (Opens a modal)
• Sampling distribution of a sample mean example (Opens a modal)
• Mean and standard deviation of sample means Get 3 of 4 questions to level up!
• Finding probabilities with sample means Get 3 of 4 questions to level up!

Sampling distributions for differences in sample means

• Sampling distribution of the difference in sample means (Opens a modal)
• Sampling distribution of the difference in sample means: Probability example (Opens a modal)
• Differences of sample means — Probability examples (Opens a modal)
• Mean and standard deviation of difference of sample means Get 3 of 4 questions to level up!
• Shape of sampling distributions for differences in sample means Get 3 of 4 questions to level up!

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Test: AP Statistics

Assigning the treatment based on who needs it the most 

Obtaining nationally representative samples for both

Assigning the treatment by gender

Flipping a coin

1/1 questions

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Random Selection vs. Random Assignment

Random selection and random assignment  are two techniques in statistics that are commonly used, but are commonly confused.

Random selection  refers to the process of randomly selecting individuals from a population to be involved in a study.

Random assignment  refers to the process of randomly  assigning  the individuals in a study to either a treatment group or a control group.

You can think of random selection as the process you use to “get” the individuals in a study and you can think of random assignment as what you “do” with those individuals once they’re selected to be part of the study.

The Importance of Random Selection and Random Assignment

When a study uses  random selection , it selects individuals from a population using some random process. For example, if some population has 1,000 individuals then we might use a computer to randomly select 100 of those individuals from a database. This means that each individual is equally likely to be selected to be part of the study, which increases the chances that we will obtain a representative sample – a sample that has similar characteristics to the overall population.

By using a representative sample in our study, we’re able to generalize the findings of our study to the population. In statistical terms, this is referred to as having  external validity – it’s valid to externalize our findings to the overall population.

When a study uses  random assignment , it randomly assigns individuals to either a treatment group or a control group. For example, if we have 100 individuals in a study then we might use a random number generator to randomly assign 50 individuals to a control group and 50 individuals to a treatment group.

By using random assignment, we increase the chances that the two groups will have roughly similar characteristics, which means that any difference we observe between the two groups can be attributed to the treatment. This means the study has  internal validity  – it’s valid to attribute any differences between the groups to the treatment itself as opposed to differences between the individuals in the groups.

Examples of Random Selection and Random Assignment

It’s possible for a study to use both random selection and random assignment, or just one of these techniques, or neither technique. A strong study is one that uses both techniques.

The following examples show how a study could use both, one, or neither of these techniques, along with the effects of doing so.

Example 1: Using both Random Selection and Random Assignment

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. Once they have the 100 individuals, they once again use a computer to randomly assign 50 of the individuals to a control group (e.g. stick with their standard diet) and 50 individuals to a treatment group (e.g. follow the new diet). They record the total weight loss of each individual after one month.

Results:  The researchers used random selection to obtain their sample and random assignment when putting individuals in either a treatment or control group. By doing so, they’re able to generalize the findings from the study to the overall population  and  they’re able to attribute any differences in average weight loss between the two groups to the new diet.

Example 2: Using only Random Selection

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 individuals to be in the study by using a computer to randomly select 100 names from a database. However, they decide to assign individuals to groups based solely on gender. Females are assigned to the control group and males are assigned to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers used random selection to obtain their sample, but they did not use random assignment when putting individuals in either a treatment or control group. Instead, they used a specific factor – gender – to decide which group to assign individuals to. By doing this, they’re able to generalize the findings from the study to the overall population but they are  not  able to attribute any differences in average weight loss between the two groups to the new diet. The internal validity of the study has been compromised because the difference in weight loss could actually just be due to gender, rather than the new diet.

Example 3: Using only Random Assignment

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 100 males athletes to be in the study. Then, they use a computer program to randomly assign 50 of the male athletes to a control group and 50 to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers did not use random selection to obtain their sample since they specifically chose 100 male athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. However, they did use random assignment, which means they can attribute any difference in weight loss to the new diet.

Example 4: Using Neither Technique

Study:  Researchers want to know whether a new diet leads to more weight loss than a standard diet in a certain community of 10,000 people. They recruit 50 males athletes and 50 female athletes to be in the study. Then, they assign all of the female athletes to the control group and all of the male athletes to the treatment group. They record the total weight loss of each individual after one month.

Results:  The researchers did not use random selection to obtain their sample since they specifically chose 100 athletes. Because of this, their sample is not representative of the overall population so their external validity is compromised – they will not be able to generalize the findings from the study to the overall population. Also, they split individuals into groups based on gender rather than using random assignment, which means their internal validity is also compromised – differences in weight loss might be due to gender rather than the diet.

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Random Sampling vs. Random Assignment

Random sampling and random assignment are fundamental concepts in the realm of research methods and statistics. However, many students struggle to differentiate between these two concepts, and very often use these terms interchangeably. Here we will explain the distinction between random sampling and random assignment.

Random sampling refers to the method you use to select individuals from the population to participate in your study. In other words, random sampling means that you are randomly selecting individuals from the population to participate in your study. This type of sampling is typically done to help ensure the representativeness of the sample (i.e., external validity). It is worth noting that a sample is only truly random if all individuals in the population have an equal probability of being selected to participate in the study. In practice, very few research studies use “true” random sampling because it is usually not feasible to ensure that all individuals in the population have an equal chance of being selected. For this reason, it is especially important to avoid using the term “random sample” if your study uses a nonprobability sampling method (such as convenience sampling).

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Random assignment refers to the method you use to place participants into groups in an experimental study. For example, say you are conducting a study comparing the blood pressure of patients after taking aspirin or a placebo. You have two groups of patients to compare: patients who will take aspirin (the experimental group) and patients who will take the placebo (the control group). Ideally, you would want to randomly assign the participants to be in the experimental group or the control group, meaning that each participant has an equal probability of being placed in the experimental or control group. This helps ensure that there are no systematic differences between the groups before the treatment (e.g., the aspirin or placebo) is given to the participants. Random assignment is a fundamental part of a “true” experiment because it helps ensure that any differences found between the groups are attributable to the treatment, rather than a confounding variable.

So, to summarize, random sampling refers to how you select individuals from the population to participate in your study. Random assignment refers to how you place those participants into groups (such as experimental vs. control). Knowing this distinction will help you clearly and accurately describe the methods you use to collect your data and conduct your study.

AP Statistics

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About the Course

Learn about the major concepts and tools used for collecting, analyzing, and drawing conclusions from data. You’ll explore statistics through discussion and activities, and you'll design surveys and experiments.

Skills You'll Learn

Selecting methods for collecting or analyzing data

Describing patterns, trends, associations, and relationships in data

Using probability and simulation to describe probability distributions and define uncertainty in statistical inference

Using statistical reasoning to draw appropriate conclusions and justify claims

Equivalency and Prerequisites

College course equivalent.

A one-semester, introductory, non-calculus-based college course in statistics

Recommended Prerequisites

A second-year course in algebra

Thu, May 8, 2025

AP Statistics Exam

This is the regularly scheduled date for the AP Statistics Exam.

About the Units

The course content outlined below is organized into commonly taught units of study that provide one possible sequence for the course. Your teacher may choose to organize the course content differently based on local priorities and preferences.

Course Content

Unit 1: exploring one-variable data.

You’ll be introduced to how statisticians approach variation and practice representing data, describing distributions of data, and drawing conclusions based on a theoretical distribution.

Topics may include:

• Variation in categorical and quantitative variables
• Representing data using tables or graphs
• Calculating and interpreting statistics
• Describing and comparing distributions of data
• The normal distribution

On The Exam

15%–23% of Score

Unit 2: Exploring Two-Variable Data

You’ll build on what you’ve learned by representing two-variable data, comparing distributions, describing relationships between variables, and using models to make predictions.

• Comparing representations of 2 categorical variables
• Calculating statistics for 2 categorical variables
• Representing bivariate quantitative data using scatter plots
• Describing associations in bivariate data and interpreting correlation
• Linear regression models
• Residuals and residual plots
• Departures from linearity

5%–7% of Score

Unit 3: Collecting Data

You’ll be introduced to study design, including the importance of randomization. You’ll understand how to interpret the results of well-designed studies to draw appropriate conclusions and generalizations.

• Planning a study
• Sampling methods
• Sources of bias in sampling methods
• Designing an experiment
• Interpreting the results of an experiment

12%–15% of Score

Unit 4: Probability, Random Variables, and Probability Distributions

You’ll learn the fundamentals of probability and be introduced to the probability distributions that are the basis for statistical inference.

• Using simulation to estimate probabilities
• Calculating the probability of a random event
• Random variables and probability distributions
• The binomial distribution
• The geometric distribution

10%–20% of Score

Unit 5: Sampling Distributions

As you build understanding of sampling distributions, you’ll lay the foundation for estimating characteristics of a population and quantifying confidence.

• Variation in statistics for samples collected from the same population
• The central limit theorem
• Biased and unbiased point estimates
• Sampling distributions for sample proportions
• Sampling distributions for sample means

7%–12% of Score

Unit 6: Inference for Categorical Data: Proportions

You’ll learn inference procedures for proportions of a categorical variable, building a foundation of understanding of statistical inference, a concept you’ll continue to explore throughout the course.

• Constructing and interpreting a confidence interval for a population proportion
• Setting up and carrying out a test for a population proportion
• Interpreting a p-value and justifying a claim about a population proportion
• Type I and Type II errors in significance testing
• Confidence intervals and tests for the difference of 2 proportions

Unit 7: Inference for Quantitative Data: Means

Building on lessons learned about inference in Unit 6, you’ll learn to analyze quantitative data to make inferences about population means.

• Constructing and interpreting a confidence interval for a population mean
• Setting up and carrying out a test for a population mean
• Interpreting a p-value and justifying a claim about a population mean
• Confidence intervals and tests for the difference of 2 population means

10%–18% of Score

Unit 8: Inference for Categorical Data: Chi-Square

You’ll learn about chi-square tests, which can be used when there are two or more categorical variables.

• The chi-square test for goodness of fit
• The chi-square test for homogeneity
• The chi-square test for independence
• Selecting an appropriate inference procedure for categorical data

2%–5% of Score

Unit 9: Inference for Quantitative Data: Slopes

You’ll understand that the slope of a regression model is not necessarily the true slope but is based on a single sample from a sampling distribution, and you’ll learn how to construct confidence intervals and perform significance tests for this slope.

• Confidence intervals for the slope of a regression model
• Setting up and carrying out a test for the slope of a regression model
• Selecting an appropriate inference procedure

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AP Statistics Course and Exam Description

This is the core document for the course. It clearly lays out the course content and describes the exam and the AP Program in general.

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AP Statistics can lead to a wide range of careers and college majors

Additional Information

Helping math teachers bring statistics to life

Chapter 4 - Day 11

Day 12 day 13, all chapters, students struggled with….

Explaining statistically significant with greater detail than “Yes because it is below 5%.”

Thinking that inference about cause-and-effect needs both random assignment and random samples.  Many students said an experiment that had random assignment but not a random sample could not determine causation because they couldn’t generalize it to the whole population.

Remedies…

Part of this issue will resolve itself throughout the year.  This is the first time students have to describe statistical significance so some error is not surprising.  Make sure to give written feedback for their responses by adding in parts that are missing.  This will help students know what you expect.

Explain that it is common in real experiments to not have a random sample.  The subjects are usually volunteers because if you did a random sample it would be very hard to convince people to come and be a part of your experiment.  So it is actually very common to have random assignment without random sample and that doesn’t mean we can’t determine causation.

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A Strategic Approach to Seating Arrangements in High School

Which seating arrangement works best—assigned, random, or something else? Here’s an idea from someone who has tried them all.

Ever ponder why it’s so hard to come up with the best seating arrangement for any given class? If you’ve done the actual math, you’ve determined that it’s improbable just by chance. If you haven’t, then you should know that in a class of 30 students with 30 seats, probability tells you there are 30! (30 factorial, or 2.6 x 10 32 ) different ways they could be seated—more ways if you are like many teachers who have over 30 students per class. Even if you’re fortunate enough to have only 15 young minds to teach in a class with one seat each, there are still over a trillion (15!) ways to arrange them.

Although only one of those many outcomes can be the best , many outcomes could be pretty good, but that also means there’s the potential for a lot of problematic arrangements for both you and your students. 

So what’s a teacher to do with so many possible outcomes—just throw your hands up and let the students choose? Leave it to random chance and hope for something reasonably good? Dedicate lots of time and thought with a more strategic and intentional approach? After decades of teaching and years of mentoring, my answers to these questions would be: not a chance, still no, and yep! Here’s a look at each of those approaches.

Student Choice?

On the first day of school in many buildings or classrooms, you’re likely to overhear (or maybe even say), “There are no assigned seats—sit wherever you want.” This, of course, is not what actually happens. Students with the most status, or bullies, or those who are early, or those whose friends got there and saved them a space, might get to sit where they want, and the rest end up sitting someplace they may never have chosen if given the chance.

If you then never create a seating chart, this imbalance is repeated on a daily basis. If you later use self-selected seats to generate a seating chart, what frequently happens is that some groups or areas work, while others do not. Then, to break up the problem groups, you also have to break up those groups or areas that aren’t a problem—not great for student-to-student relationships or for teacher-to-student relationships.

This took me over a decade to realize on my own, and then I finally recognized that my frustrations with my students’ choices were really my own frustrations over not learning from my mistakes. Of course, their social priorities did not match my educational priorities. So, not a chance I’d keep using self-selection with their still-developing adolescent frontal lobes.

Random Assignment?

How about using randomness to solve some of the problems created by choice seating? Regardless of class size, if you run repeated random groupings of three or four students, you will see that more often than not, you will end up with quite a few well-mixed groups but also one or two “stronger” groups and one or two “weaker” groups. This is both problematic and not your original intent.

If you’re relying on high-tech random seating chart generators or even low-tech methods like drawing names for extended seating assignments, especially if those assignments are in groups, you are likely making things harder for both yourself and many of your students. So, a randomized approach for your day-to-day base seating? Still a no. Save randomization for short, frequent visible learning opportunities (as in Peter Liljedahl’s Building Thinking Classrooms in Mathematics, Grades K-12 ) or other more appropriate situations. 

Strategic Seating?

An early investment in strategic seating based on intentionality and data can pay big dividends. This method worked well for me with Biology I (a required course for all ninth-grade students when I taught it), Marine Biology (a semester elective with students ranging from ocean-loving geeks to those whose reply to “Why did you elect to take this class?” was “I didn’t—my counselor put me in here”), and AP Statistics, which is where I first experimented with it.

Here’s what prompted the more strategic and intentional approach on my part many years ago. In my first few years, I assumed that the junior and senior AP Statistics students coming to my class after taking AP Calculus, Pre-calculus, or Trigonometry the previous year would be mature and motivated enough to choose where they wanted to sit, and of course I was wrong, because their choices were still more along the lines of social reasons than academic ones.

This frequently resulted in table groups of four based on friends from their previous math classes. The common result was the Calc groups soared, the Pre-calc groups did well enough, and the Trig groups struggled—definitely not the result I was striving to achieve.

So I employed data about each student’s previous math class, other academic performance, and grade level to create groups that had one or two from each course in them and used that as my starting seating chart on the first day of school. I eventually did something similar with my Biology and Marine Biology students by looking at their past academic performance as well as other data such as individualized education programs and 504s.

This initial setup took a lot of time but usually paid off fairly quickly because I spent way less time having to deal with the problems that nearly always resulted from choice or random seating. Additionally, I used that data for shuffling for new groups at the end of a time period such as a unit. Depending on how a given class was proceeding, I would get data from the students after we had successfully established routines for success.

From these strategic seating arrangements, I could orchestrate a variety of ways to quickly shuffle groups for sharing information, teaming for quizzes , tackling new tasks, or building classroom community. So, yep!—strategic and intentional (and initially very time-consuming) seating was my go-to for the last couple of decades of my career. If you aren’t using seating charts at all and need some more convincing, this article may help.

In The Trenches: Teven Jenkins Was A Beast in the Bears’ Preseason Win

While it was only a small sample size in this matchup against the Bills , Bears left guard Teven Jenkins put a few really nice plays on tape.

The Bears’ offensive line will have a massive say in how far the team can go this season. We know the skill position players are there. We know the defense will be solid. We’re pretty sure that, while there may be some growing pains, the quarterback can be very good. Whether or not this offense reaches its ceiling may ultimately come down to line play.

Each week, I’ll do my best to break down the offensive line film and spotlight either a few plays or a specific player that stood out to me. If you’re into an in-depth Bears tape breakdown, Patrick does a great job each week of that as well, taking a look at the whole game .

Let’s take a look at a few plays starring Teven Jenkins that stuck out in the preseason performance on Saturday.

One note I’d like to mention before picking out a few plays: While most of us who watch the film can analyze technique or make an educated guess at what an assignment might be on a certain play, none of us actually know with 100% certainty what the assignment is for each player on every play.

Teven Jenkins Stands Out

This was the Bears’ second offensive play of the game. After their run on 1st and 10 didn’t get far, Shane Waldron opted to throw the ball. It’s a pretty standard 3/4 slide to the left, which means the LT, LG, C, and RG all slide a gap left while the RT is on an island against the end.

Jenkins, to start, has a three-technique lined up in his gap. He has a very good first step, his man slants inside, and instead of turning and following him in, Jenkins does a great job passing him off to Coleman Shelton and then looking back to his gap. In this case, since there’s no backer blitzing he has to worry about, Jenkins goes and helps Braxton Jones by buying A.J. Epenesa. It’s pretty much textbook on how to handle a slant on the pass rush, and the physicality to end the play was a cherry on top.

Okay, so this is the very next play. Darnell Wright took a holding penalty the play before, so the Bears have about 2nd and 19. Shane Waldron calls a draw. LT, RG, and RT all take their pass sets to sell the fake. LG and C take quick sets since they have to cover up/double-team the DT in between them lined up in a 2i. Jenkins and Shelton do a great job going from a quick pass set and turning that into a double-team run block.

Shelton is on the double for the first few steps but probably leaves a little bit early to cover up the linebacker. The LB didn’t really make Jenkins or Shelton make a choice yet, but Shelton leaves the double early, which actually allows the LB to make the play coming over the top, though the corner came flying in, too. Had they stayed on the double team a touch longer, Jenkins would have likely been the man to come off, and maybe the play would have picked up a few extra yards.

What’s impressive about Jenkins here, though, is that despite his man leaving early, he does an amazing job of keeping his feet moving while not burying himself in the block. The DT tries to shed Jenkins, but it’s too late. His hands are locked on the inside of those shoulder pads (totally legal, definitely not holding), and he keeps running his feet. He finishes the play with a pancake.

Ok, I know this play doesn’t go for very much, but again, we’re working with a limited sample size from the starters, but also, I just love a perfectly executed reach block. The Bears are running outside-zone to the left. On outside-zone, every lineman’s job is to cover up and try to seal the play-side shoulder of the defender in their zone. Since it’s outside zone left, each OL’s zone is the gap to their left on the first level, and if no one is there, move up to the second level and try to cut off a linebacker.

The play does not work because Darnell Wright and Coleman Shelton were each a touch slow. Cutting off a backer flowing with the run is a tough block, so it’s not necessarily an egregious mistake on their part.

But Teven Jenkins has a tough assignment here. He’s got a three-technique lined up outside of his play-side shoulder, and he’s got to reach block him. His goal is to get his head across the defenders and seal his left shoulder. Jenkins’ first step is perfect, he’s so quick off the ball. By the time the DL gets out of his stance, Jenkins has already made up the ground, got hands-on, and kept his feet moving to turn and seal the DL, so he can’t make the play.

It’s a common block for linemen to make, but it’s a tough one to execute perfectly, especially with the DL getting essentially a half-gap head start. Jenkins did that here.

After the seal, running back Khalil Herbert has a hole you could drive a car through on the first level. The linebackers coming over the top made a play at the second level, but still, the reach block was perfectly executed and gave the play a chance to work.

Bengals Won’t Play Starters This Week — What Does That Mean For the Bears?

Around the nfl: nabers ankle injury, niners scrap joint practices, reddick wants a trade, more, caleb williams was preseason week 1’s best passer, let’s talk about bears running back khalil herbert, who might be expendable, haason reddick has requested a trade from the new york jets.

Matt is from the Chicagoland area and has been working in Chicago sports since 2015 with stops at WGN Radio, the Chicago Blackhawks, Stadium, and NBC Sports Chicago prior to landing at Betsperts. Matt covers just about everything for Betsperts and Bleacher Nation but focuses on the NHL and college football.

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