An experiment imposes treatments on experimental units and measures a response, which lets you establish cause and effect when it is well designed. The four pillars of a well-designed experiment are comparison, random assignment, replication, and control of confounding variables.
Types of Experimental Design in AP Stats
In AP Statistics, the main experimental designs are completely randomized design, randomized block design, and matched pairs design. A completely randomized design assigns treatments to all experimental units at random. A randomized block design groups similar units first, then randomizes treatments within each block. A matched pairs design is a special type of block design where each pair is matched on relevant traits, or each subject receives both treatments.
For any design, identify the experimental units, treatments, response variable, and possible confounding variables. Then explain how random assignment, comparison, replication, and control help make a cause-and-effect conclusion reasonable.
Why This Matters for the AP Statistics Exam
Experimental design shows up across multiple-choice and free-response questions in AP Statistics. You will be asked to identify the components of a study, decide whether a design is well constructed, and explain why a particular design works for a situation. Later units build on this: the reason you can say a treatment "caused" an effect comes directly from random assignment in a well-designed experiment.
A common exam task is to describe or critique an experiment. When you do that, use precise language. Random assignment is for experiments and causation. Random selection is for samples and generalizing to a population. Mixing those up is one of the easiest ways to lose points.
Key Takeaways
- Experimental units are who or what gets the treatments; explanatory variables (factors) are what you manipulate, and their levels or combinations are the treatments.
- The response variable is the outcome you measure after treatments are applied.
- A confounding variable is linked to the explanatory variable and also affects the response, which can fake an association.
- A well-designed experiment has comparison of at least two treatment groups, random assignment, replication, and control of confounding variables.
- Completely randomized, randomized block, and matched pairs are the main designs; matched pairs is a special case of blocking.
- Causation is possible in experiments because the treatment is imposed and randomly assigned.
Components of an Experiment
An experiment imposes treatments on individuals and measures the result, which is what separates it from an observational study where treatments are not imposed.
The experimental units are the individuals or objects that are assigned treatments. These may be people, animals, plants, or other objects of study. When the experimental units are people, they are often called participants or subjects.
The explanatory variable (also called a factor) is the variable whose levels are manipulated on purpose. The levels or combinations of levels of the explanatory variable are the treatments.
The response variable is the outcome measured after the treatments have been administered. It is what you are actually studying.
Example
Say you want to study the effects of different types of exercise on weight loss. The explanatory variable is the type of exercise (running, swimming, lifting weights), and those types are the treatments. The response variable is the amount of weight loss. The experimental units are the people assigned to each treatment, and you measure their weight loss after the treatments are applied.
By manipulating the explanatory variable and measuring the response variable, you can study whether different types of exercise lead to different amounts of weight loss.
Confounding
A confounding variable is related to the explanatory variable and also influences the response variable. Because it is tangled up with the explanatory variable, it can create a false perception of association, making it hard to tell what really caused the response.
In the exercise example, factors like age, diet, and genetics could be confounding variables. If the people who ran also happened to eat healthier diets, you could not tell whether the weight loss came from running or from the diet. Good experimental design uses random assignment to spread these uncontrolled variables across treatment groups, so differences in the response can be attributed to the treatments themselves.
Elements of a Well-Designed Experiment
A well-designed experiment should include these four elements:
- Comparison of at least two treatment groups, one of which could be a control group. Comparing responses across treatments lets you see differences caused by the treatments. A control group does not receive the treatment of interest and serves as a baseline.
- Random assignment of treatments to experimental units. Random assignment tends to balance out uncontrolled variables across groups, so observed differences can be tied to the treatments rather than to other factors.
- Replication (more than one experimental unit in each treatment group). Having multiple units per group means results are not driven by one unusual individual and gives you enough data to see real patterns.
- Control of potential confounding variables where appropriate. Keeping conditions consistent or using blocking helps limit the influence of variables you are not studying.
A quick way to remember the strategy: control what you can, block on what you cannot control, and randomize to create comparable groups.
Control Groups and Placebos
A control group is a set of experimental units either not given the treatment of interest or given a treatment with an inactive substance (a placebo), so you can tell whether the treatment of interest actually has an effect.
A placebo is a treatment with no active ingredient that otherwise looks like the real treatments. Sometimes a placebo group does not make sense for a given experiment.
The placebo effect happens when subjects respond to a placebo, even though it has no active ingredient. This is one reason control and placebo groups are useful.
Types of Experiments
Blind Experiments
In a single-blind experiment, the subjects do not know which treatment they are receiving, but the research team does, or the other way around. One side knows, not both.
In a double-blind experiment, neither the subjects nor the members of the research team who interact with them know which treatment a subject is receiving. This helps avoid personal bias from creeping into how the response is measured or how subjects react.
Completely Randomized Design
In a completely randomized design, treatments are assigned to experimental units completely at random. Random assignment tends to balance the effects of uncontrolled variables, so differences in responses can be attributed to the treatments. Group sizes will not always be exactly even.
This is the simplest design. When there are clear groupings or similarities among the units that could affect the response, a more structured design may work better.
Ways to randomly assign treatments include using a random number generator, a table of random values, or drawing chips without replacement.
Randomized Block Design
In a randomized complete block design, treatments are assigned completely at random within each block. Blocking groups experimental units that are similar with respect to a blocking variable, so you can separate natural variability from differences caused by the treatments.
For example, in an experiment on different fertilizers and plant growth, soil type could be a blocking variable. You divide the plants into blocks by soil type, then randomly assign the fertilizers within each block. That way differences in soil type do not muddy your results.
The figure below shows an example of assigning treatments within blocks in the context of students and exam results:
Matched Pairs
A matched pairs design is a special case of a randomized block design. Subjects (people or other objects of study) are arranged in pairs matched on relevant factors like age or other characteristics. Pairs may form naturally or be created by the experimenter.
Every pair receives both treatments. You randomly assign one treatment to one member of the pair and the other treatment to the second member. Alternately, each subject may receive both treatments. This setup lets you compare responses to the two treatments while keeping the matched factors similar.
How to Use This on the AP Statistics Exam
Free Response
When a question asks you to describe an experiment, name the experimental units, explain how you will randomly assign treatments, list the treatments, and state the response variable you will measure. Be specific to the context of the problem rather than using generic terms.
When asked whether an experiment is well designed, check it against the four elements: comparison, random assignment, replication, and control of confounding. Point to the specific feature that is present or missing.
Common Trap
Random assignment and random selection are not interchangeable. Write about random assignment when you are talking about experiments and whether a treatment caused an effect. Write about random selection when you are talking about generalizing sample results to a population. Using the wrong one in your explanation is an easy way to lose credit.
Explaining Confounding
If you claim a variable is confounding, explain how it is connected to both the explanatory variable and the response variable in that specific situation. A vague statement that "there could be confounding" is not enough.
Common Misconceptions
- Confounding and causation: A confounding variable does not just affect the response. It is also tied to the explanatory variable. If a variable affects the response but is not linked to the explanatory variable, it is not confounding in the way the term is used here.
- Control group means no treatment at all: A control group can receive a placebo or a standard treatment, not necessarily nothing. The point is to have a baseline for comparison.
- Random assignment makes groups identical: It does not guarantee identical groups. It balances out uncontrolled variables on average across groups, which is what lets you attribute differences to the treatments.
- Blinding is about secrecy for its own sake: Blinding exists to reduce bias in how responses are measured and how subjects react, not just to hide information.
- Matched pairs is totally different from blocking: Matched pairs is a special case of a randomized block design, with pairs acting as the blocks.
- Replication means repeating the whole experiment: In this context, replication means having more than one experimental unit in each treatment group, not necessarily rerunning the entire study.
zed design, randomized block design, and matched pairs design. Completely randomized designs assign treatments to all experimental units at random, randomized block designs group similar units first, and matched pairs designs compare paired units or two treatments on the same unit.
What is an experimental unit in AP Stats?
An experimental unit is the person, object, animal, plant, or other item that receives a treatment in an experiment. If the experimental units are people, they are often called subjects or participants.
What is the difference between random assignment and random selection?
Random assignment is used in experiments to assign treatments to experimental units, which supports cause-and-effect conclusions. Random selection is used in sampling to choose individuals from a population, which supports generalizing results to that population.
What is a randomized block design?
A randomized block design groups experimental units by a variable that may affect the response, then randomly assigns treatments within each block. Blocking helps control known sources of variability before random assignment happens.
What is a matched pairs design?
A matched pairs design is a special type of randomized block design. Each pair is matched on important traits, or each subject receives both treatments, so the comparison focuses more directly on the treatment effect.
Why does random assignment matter in experiments?
Random assignment helps balance uncontrolled variables across treatment groups. That makes it more reasonable to attribute differences in the response variable to the treatments instead of to confounding variables.
Related AP Statistics Guides
Vocabulary
The following words are mentioned explicitly in the College Board Course and Exam Description for this topic.Term | Definition |
|---|---|
blocking | A technique that groups experimental units into blocks where units within each block are similar with respect to at least one blocking variable. |
blocking variable | A variable used to group experimental units into blocks so that natural variability can be separated from differences due to that variable. |
completely randomized design | An experimental design where treatments are assigned to experimental units completely at random to balance the effects of confounding variables. |
confounding variable | A variable that is related to the explanatory variable and influences the response variable, potentially creating a false perception of association between them. |
control group | A group in an experiment that receives no treatment or a standard/baseline treatment, used as a reference for comparison. |
double-blind experiment | An experiment where neither the subjects nor the members of the research team who interact with them know which treatment a subject is receiving. |
experimental unit | The participants or subjects to which treatments are assigned in an experiment. |
explanatory variable | A variable whose values are used to explain or predict corresponding values for the response variable. |
factor | An explanatory variable in an experiment whose levels are manipulated intentionally. |
matched pairs design | A special case of a randomized block design where subjects are arranged in pairs matched on relevant factors, and each pair receives both treatments. |
participant | Human subjects or individuals who are assigned treatments in an experiment. |
placebo | An inactive substance given to a control group to determine if a treatment of interest has an effect. |
placebo effect | A response to a placebo that occurs when experimental units react to receiving a treatment, even though the treatment is inactive. |
random assignment | The process of randomly allocating experimental units to different treatment groups to ensure unbiased distribution and reduce bias. |
randomized complete block design | An experimental design where treatments are assigned completely at random within each block to control for a blocking variable. |
replication | The use of multiple experimental units in each treatment group to increase reliability and reduce the effect of random variation. |
response variable | A variable whose values are being explained or predicted based on the explanatory variable. |
single-blind experiment | An experiment where subjects do not know which treatment they are receiving, but members of the research team do, or vice versa. |
treatment | Different conditions assigned to experimental units in an experiment. |
treatment groups | Distinct groups in an experiment that receive different treatments or conditions being compared. |
Frequently Asked Questions
What are the types of experimental design in AP Stats?
The main types are completely randomized design, randomized block design, and matched pairs design. Completely randomized designs assign treatments to all experimental units at random, randomized block designs group similar units first, and matched pairs designs compare paired units or two treatments on the same unit.
What is an experimental unit in AP Stats?
An experimental unit is the person, object, animal, plant, or other item that receives a treatment in an experiment. If the experimental units are people, they are often called subjects or participants.
What is the difference between random assignment and random selection?
Random assignment is used in experiments to assign treatments to experimental units, which supports cause-and-effect conclusions. Random selection is used in sampling to choose individuals from a population, which supports generalizing results to that population.
What is a randomized block design?
A randomized block design groups experimental units by a variable that may affect the response, then randomly assigns treatments within each block. Blocking helps control known sources of variability before random assignment happens.
What is a matched pairs design?
A matched pairs design is a special type of randomized block design. Each pair is matched on important traits, or each subject receives both treatments, so the comparison focuses more directly on the treatment effect.
Why does random assignment matter in experiments?
Random assignment helps balance uncontrolled variables across treatment groups. That makes it more reasonable to attribute differences in the response variable to the treatments instead of to confounding variables.