AP Statistics – Unit 3: Collecting Data

1.

Individuals & Variables

  • Individuals: the objects/people being described.

  • Variables:

    • Categorical → groups/labels (ex: color, gender, zip code).

    • Quantitative → numbers with meaning (ex: height, income).

      • Discrete: countable (ex: # of pets).

      • Continuous: measurable (ex: weight, time).

2.

Populations, Samples, and Parameters

  • Population → entire group of interest.

  • Sample → subset of population actually studied.

  • Parameter → numerical fact about a population (μ, p).

  • Statistic → numerical fact from a sample (x̄, p̂).

💡 Trap: Watch wording. If they say “mean height of all students,” that’s a parameter. If they say “mean height of the sample of students surveyed,” that’s a statistic.

3.

Sampling Methods

a)

Good Methods

  • Simple Random Sample (SRS) → every group of n individuals equally likely.

  • Stratified Random Sample → split population into homogeneous groups (strata), take SRS from each.

  • Cluster Sample → split population into clusters, randomly select clusters, sample everyone in chosen clusters.

  • Systematic Sample → pick every k-th individual after a random start.

  • Multistage Sample → mix methods.

b)

Bad Methods

(Bias sources)

  • Convenience Sampling → easy-to-reach individuals.

  • Voluntary Response Sampling → individuals choose themselves (usually strong opinions).

💡 Bias Types:

  • Undercoverage (some groups left out).

  • Nonresponse (individuals selected but don’t respond).

  • Response bias (wording of question, interviewer influence, lying).

4.

Observational Studies vs. Experiments

  • Observational Study → measures variables, doesn’t impose treatments.

  • Experiment → deliberately imposes treatment to measure response.

💡 Key difference: Only experiments can show cause-and-effect, not observational studies.

5.

Experiments: Design Principles

  • Explanatory variable (factor) → what you change.

  • Response variable → what you measure.

  • Treatments → combinations of factors/levels.

  • Experimental units → subjects (individuals).

Good experiment design:

  1. Comparison → 2+ treatments.

  2. Random assignment → eliminates confounding.

  3. Control → keep conditions the same for all groups.

  4. Replication → large sample sizes so differences aren’t chance.

Control Types:

  • Placebo → fake treatment to test placebo effect.

  • Blinding → subject doesn’t know treatment.

  • Double-blind → subject + experimenter both don’t know.

6.

Confounding vs. Lurking Variables

  • Confounding variable → affects response, related to explanatory variable, can’t separate effects.

  • Lurking variable → hidden variable not included but influences results.

8.

Experimental Designs

  • Completely Randomized Design → all subjects randomly assigned to treatments.

  • Randomized Block Design → subjects grouped into blocks (similar individuals), randomization occurs within blocks.

  • Matched Pairs Design → special block design:

    • Each subject receives both treatments (order randomized), OR

    • Subjects paired, each gets different treatment.

9.

AP Exam Free Response Expectations

When describing an experiment or sample design:

  • Identify population

  • Explain how randomization is done

  • Mention control, replication, and comparison

  • Avoid vague words (“randomly chosen”) — describe the actual method

📝 PRACTICE CHECK

Multiple Choice

  1. A company surveys every 10th person leaving a store. This is:
    a) SRS
    b) Stratified
    c) Systematic
    d) Cluster

  2. A researcher wants to test a new fertilizer on tomato growth. Half the plants are randomly assigned to fertilizer, half to water. The explanatory variable is:
    a) Fertilizer vs. water
    b) Tomato growth
    c) Type of tomato plant
    d) Sunlight

  3. Which method suffers most from response bias?
    a) Online poll on political website
    b) Random digit dialing
    c) Census
    d) Cluster sample

FRQ-Style

Q: Researchers want to know if background music improves test performance. Design an experiment.

  • Identify explanatory & response variables.

  • Explain random assignment.

  • Describe control group.

  • State how to measure response.

  • Explain how results could show cause-and-effect.

7.

Sampling & Experimental Design Traps

  • If asked to “describe how to select an SRS,” you must number individuals, randomize with calculator/table, then choose sample.

  • If asked “can we conclude cause-and-effect?” → ONLY if random assignment.

  • If asked “can we generalize to population?” → ONLY if random sampling.