Unit 3: Collecting Data
AP Statistics: 51 practice questions with detailed explanations.
Unit Study Guide
Executive Summary
How data is collected decides what conclusions are valid. Random sampling enables generalization; random assignment enables causation.
Sampling
A census measures everyone; a sample measures a subset. Simple random samples give every individual an equal chance. Stratified samples take random draws within groups; cluster samples measure everyone in randomly chosen groups; systematic picks every kth. The sampling frame is the list you draw from — undercoverage misses groups not on it.
Bias
Convenience and voluntary-response samples skew. Nonresponse bias: those who answer differ from those who don't. Response bias: wording or lying distorts answers. Bigger samples reduce variability but never fix bias.
Experiments
Experiments impose treatments; observational studies only watch. Random assignment spreads lurking variables across groups, enabling causal conclusions. Control groups provide comparison; placebos and blinding prevent expectation effects; blocking groups similar subjects; matched pairs use each subject as its own control.
Inference
Random sampling → generalize to the population. Random assignment → cause-and-effect. Confounding: two variables' effects can't be separated. Replication (many subjects) reduces chance variation.
Exam traps
Sampling and assignment solve DIFFERENT problems — don't mix them up. Larger samples do not remove bias. Observational studies cannot prove causation.