AP Statistics Unit 3: Collecting Data
Sampling methods, bias and experimental design.
Unit overview
How data are collected decides what conclusions are allowed. A well-designed sample lets you generalise to the population; a well-designed experiment lets you conclude cause and effect. Observational studies can show association but cannot establish causation, because lurking variables may explain the pattern.
Random sampling methods include simple random samples, stratified samples (random samples within similar groups) and cluster samples (randomly chosen whole groups). Experiments need comparison, random assignment of treatments, replication and control of other variables. Blocking groups similar units before random assignment to reduce variability.
Key topics
- Sampling methods
- Simple random, stratified, cluster and systematic samples, and when each is efficient.
- Bias
- Undercoverage, nonresponse, response bias and voluntary response distort estimates in a consistent direction.
- Experimental design
- Completely randomised and randomised block designs, matched pairs, control groups and placebos.
- Scope of inference
- Random sampling supports generalising; random assignment supports causal conclusions.
Common mistakes
- Confusing random sampling (who is in the study) with random assignment (who gets which treatment).
- Saying a larger sample fixes bias. More responses from a biased method still give a biased estimate.
- Describing a block design without explaining why the blocking variable is related to the response.
Exam tips
- When asked to describe randomisation, give a method someone else could follow: label units, use a random number generator, ignore repeats, assign the first half to treatment A.
- State the direction of a bias: say whether it would make the estimate too high or too low and why.
More practice on this site
- Descriptive Statistics Study Guide (study guide)
- Statistics Formulas cheat sheet (one-page formulas)
- Descriptive Statistics Quiz (quick quiz)
- Statistics practice problems (with worked solutions)
See the AP Statistics exam format and every unit on the course page.