An experiment imposes treatments on experimental units and measures a response. In the revised Unit 1 sequence, this topic focuses on what makes that experiment well designed: comparison, random assignment, replication, and control, plus the major design structures you need to recognize on the AP exam.
Why This Matters for the AP Statistics Exam
This topic is where AP Statistics moves from identifying study types to evaluating whether an experiment actually supports a strong conclusion. On the exam, you may need to identify the components of an experiment, decide whether it is well designed, choose an appropriate design, or explain why a study does or does not support a cause-and-effect claim.
Key Takeaways
- Experimental units are who or what gets the treatments.
- The explanatory variable, or factor, is what you manipulate, and the treatments are its levels or combinations of levels.
- The response variable is the outcome you measure after treatments are applied.
- A well-designed experiment has comparison, random assignment, replication, and control of confounding variables.
- Completely randomized, randomized block, and matched pairs are the main designs.
- 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.
- The experimental units are the individuals or objects assigned treatments.
- The explanatory variable is the variable whose levels are imposed on purpose.
- The treatments are the levels or combinations of levels of the explanatory variable.
- The response variable is the outcome measured after treatment.
Elements of a Well-Designed Experiment
A well-designed experiment should include:
- comparison of at least two treatment groups
- random assignment of treatments to experimental units
- replication, meaning more than one unit per treatment
- control of potential confounding variables
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, Placebos, and Blinding
A control group is used for comparison. It may receive no treatment, a standard treatment, or a placebo.
A placebo is an inactive treatment that otherwise looks like the real one. The placebo effect is the response subjects show even when the treatment has no active ingredient.
In a single-blind experiment, one side does not know which treatment is being used. In a double-blind experiment, neither the subjects nor the researchers interacting with them know.
Main Experimental Designs
Completely Randomized Design
Treatments are assigned to all experimental units completely at random. This is the simplest design and works well when no special grouping variable needs to be controlled.
Randomized Block Design
Experimental units are first sorted into blocks based on a variable known to influence the response. Treatments are then randomly assigned within each block. Blocking reduces unwanted variability from a known source.
Matched Pairs Design
A matched pairs design is a special case of a randomized block design. Units are paired based on similar characteristics, or each unit receives both treatments in random order.
How to Use This on the AP Statistics Exam
Free Response
When asked to describe an experiment:
- Name the experimental units.
- State the treatments.
- Explain how treatments will be randomly assigned.
- Identify the response variable.
- Mention relevant control, blocking, or blinding choices.
Common Trap
Random assignment and random selection are not interchangeable. Random assignment supports causation. Random selection supports generalization.
Common Misconceptions
- A control group means no treatment at all. It may receive a placebo or standard treatment instead.
- Random assignment makes groups identical. It does not; it just tends to balance uncontrolled variables.
- Matched pairs is unrelated to blocking. It is actually a special case of blocking.
- Replication means repeating the entire study. In this context, it means using more than one unit per treatment.
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.