AP Statistics - chapter 4

Population vs. Sample

• Population = the entire group you want information about.

• Sample = the subset you actually collect data from.

Convenience sample

• Choosing individuals who are easy to reach.

• Bias: likely unrepresentative (certain types of people are easier to reach).

Voluntary response sample

• People choose themselves by responding (online poll, phone-in poll).

• Bias: people with strong opinions respond → usually negative.

A simple random sample (SRS) 

every group of size n has equal chance.

How to Take an SRS

• Slips of paper

• Technology random generator

• Table of random digits (ignore repeats & labels not used)

Stratified sample

• Break population into homogeneous groups (strata), like grade level or gender.

• Take SRS within each stratum.

Helps reduce variability.

Cluster sample

• Break into heterogeneous groups that look like mini-populations (e.g., classrooms).

• Randomly select entire clusters, sample everyone in them.

Good for convenience.

Sources of Bias

• Undercoverage - Some people can’t be chosen (e.g., homeless left out of phone survey)

• Nonresponse - People selected don’t answer

• Response Bias - People lie or are influenced (drugs, illegal behavior)

• Question Wording - Leading or confusing wording pushes certain answers

Observational study

no treatment imposed → cannot determine causation

Experiment

treatment imposed → can determine causation

Confounding

Two variables’ effects on the response cannot be distinguished (If something else could explain the result → confounding)

Key Experimental Terms

• Experimental units = individuals receiving treatments (subjects if human).

• Treatment = specific condition applied.

• Explanatory variable = what’s being changed.

• Response variable = what’s being measured.

Principles of Experimental Design

• Comparison of ≥ 2 treatments

• Random assignment (balances lurking variables!)

• Control (keep conditions same except treatment)

• Replication (enough units)

Completely Randomized Design

Everyone is randomly assigned to treatments with no grouping beforehand.

Placebo effect

subjects improve simply because they think they’re receiving treatment.

Single-blind

subjects OR evaluators don’t know

Double-blind

both don’t know

Statistical Significance

An effect is statistically significant if it is unlikely to happen by chance.

Blocking

• Groups experimental units by a variable that affects response.

• Reduces variability.

Random assignment happens within each block.

Matched pairs

Two types:

1. Two very similar subjects → one gets treatment A, the other B (random who gets what).

2. One subject gets both treatments in random order.