AP Statistics Unit 3: Collecting Data
Study sampling methods, experiments, observational studies, bias, randomization with exam-format practice and rubric-based scoring.
Start AP Stats Practice · Full Study Guide
AP and Advanced Placement are trademarks of College Board. AimFive is not affiliated with or endorsed by College Board.
Inside This Unit: The Full Breakdown
This unit covers how data are collected: sampling methods for surveys and experimental design for studies. The method of data collection determines what conclusions you can draw.
Why it matters
AP Statistics free-response questions frequently ask you to design a study or critique a data collection method. Understanding the difference between observational studies and experiments — and the role of randomization — is critical for the investigative task.
Key concepts
- Simple random samples give every individual an equal chance of selection, reducing bias.
- Stratified, cluster, and systematic sampling are alternatives with specific advantages.
- Experiments use random assignment to treatment groups to establish cause and effect.
- Confounding variables are controlled through random assignment, blocking, and blinding.
Sampling Methods
A simple random sample (SRS) selects individuals so that every possible sample of size n is equally likely. This eliminates selection bias. Stratified sampling divides the population into homogeneous groups (strata) and takes an SRS from each. Cluster sampling divides the population into groups (clusters) and randomly selects entire clusters. Systematic sampling selects every kth individual from a list. Each method has trade-offs between cost, convenience, and precision. Voluntary response and convenience samples are biased and should be avoided.
Experimental Design
An experiment imposes treatments on subjects to measure their effect. Random assignment to treatment groups ensures that confounding variables are approximately balanced across groups, allowing causal conclusions. A completely randomized design assigns all subjects randomly to treatments. A randomized block design first groups subjects by a blocking variable (like age or gender) and then randomly assigns within each block. Control groups, placebos, and blinding reduce bias in measuring treatment effects.
Observational Studies and Scope of Inference
Observational studies observe subjects without imposing treatments. They can reveal associations but cannot prove causation because confounding variables may explain the relationship. The scope of inference depends on how data were collected: random sampling supports generalizing to the population, while random assignment supports causal conclusions. Only a randomized experiment with random selection from the population supports both. Most real studies achieve one or the other, not both.
AP exam tip
When designing an experiment on the AP exam, always specify: the treatments, the response variable, random assignment to groups, and what will be compared. Mention blinding and replication if applicable.
Connections to other units
- Unit 1-2: The quality of descriptive statistics and regression depends entirely on how data were collected.
- Unit 5: Sampling distributions assume random sampling — the results are invalid without it.
- Unit 6-9: All inference procedures assume data came from a random process (random sample or random assignment).
