# Sampling & Experimentation — AP Statistics
How data is collected determines what conclusions can be drawn. AP Statistics tests your understanding of sampling methods, experimental design, and the distinction between observational studies and experiments.
Key Concepts
Observational Study vs. Experiment
- Observational study: researcher observes without intervention. Cannot establish causation.
- Experiment: researcher applies a treatment. Can establish causation (with proper design).
Sampling Methods
- Simple Random Sample (SRS): every subset of size is equally likely.
- Stratified Random Sample: divide population into strata, SRS within each.
- Cluster Sample: divide into clusters, randomly select entire clusters.
- Systematic Sample: every th individual from a list.
- Convenience Sample: not random — biased!
Sources of Bias
- Selection bias: some groups are under/overrepresented.
- Response bias: answers are influenced by question wording, social pressure, etc.
- Nonresponse bias: those who don't respond differ from those who do.
- Voluntary response bias: only strongly opinionated people respond.
Principles of Experimental Design
- Control: compare treatment to a control group.
- Randomization: randomly assign subjects to groups.
- Replication: use enough subjects to detect differences.
Additional Design Features
- Blinding: subjects don't know which group they're in.
- Double-blind: neither subjects nor researchers know.
- Placebo: fake treatment for the control group.
- Blocking: group similar subjects together before random assignment (reduces variability).
Confounding Variables
A confounding variable is associated with both the explanatory and response variables, making it impossible to isolate the effect.
Scope of Inference
| Random Selection | No Random Selection | |
|---|---|---|
| Random Assignment | Causal + Generalizable | Causal only |
| No Random Assignment | Generalizable only | Neither |
Worked Example
Problem: A study finds coffee drinkers have lower rates of depression. Can we conclude coffee prevents depression?
Answer: No — this is an observational study. Confounding variables (e.g., social habits, income) could explain the association. An experiment would be needed for causation.
Practice Questions
1. A researcher surveys people at a gym about exercise habits. What type of bias might occur?
Selection bias — gym-goers are not representative of the general population.
2. Explain why randomization is important in experiments.
Randomization balances known and unknown confounding variables across treatment groups, allowing us to attribute differences to the treatment.
3. A study uses blocking by age group before assigning treatments. Why?
Blocking reduces variability due to age, making it easier to detect the treatment effect.
Want to check your answers and get step-by-step solutions?
Summary
- Experiments → causation. Observational studies → association only.
- Random selection → generalizability. Random assignment → causation.
- Good sampling avoids bias; good experiments use control, randomization, and replication.
- Confounding variables are the main threat to causal conclusions.