Unit 3: Collecting Data - AP Statistics

Observational Studies

• Retrospective Studies: Examine existing data.
• Prospective Studies: Track individuals into the future.
  • Example: Ebola epidemic studies
    • Retrospective: Timing, numbers, and locations of cases.
    • Prospective: Ongoing surveillance to limit future epidemics.

Advantages and Disadvantages

• Retrospective
  • Pros: Quicker, less expensive, less control.
  • Cons: Rely on past records, potential for inaccurate data.
• Prospective
  • Pros: Greater accuracy, monitor specific variables.
  • Cons: Expensive, time-consuming.

Bias in Sampling

• Bias: Invalidates samples, affects conclusions.
• Sampling Method Bias: Consistently unrepresentative samples.
• Voluntary Response Surveys: Overemphasize strong opinions.
• Convenience Surveys: Non-representative data.
• Undercoverage Bias: Inadequate group representation.
• Response Bias: Misleading question results.
• Nonresponse Bias: Low response rates, unclear population representation.
• Quota Sampling Bias: Non-random, potentially biased selection.
• Question Wording Bias: Poorly worded questions lead to biased responses.

Example 3.2

• Military Times survey: Voluntary, undercoverage bias likely.

Sampling Methods

• Census: Data from every individual.
• Simple Random Sample (SRS): Equal chance for selection using random generation.
  • Advantages: Easy data interpretation, minimal advance knowledge.
  • Disadvantages: Requires comprehensive list of subjects, potential for time-consuming.
• Stratified Sampling: Dividing population into strata.
  • Pros: Reduced variability, highlights group differences.
  • Cons: Difficult with large populations, forced subdivisions.
• Cluster Sampling: Dividing into clusters, sampling all in selected clusters.
  • Pros: Quick, larger sample size.
  • Cons: Less precision, potential biased selection.
• Systematic Sampling: Picking every kth individual from ordered list.
  • Pros: Simplified implementation.
  • Cons: Biased if periodic list structure.

Example 3.4

• Chicago school survey: Systematic, stratified, or cluster sampling alternatives.

Sampling Variability

• Sampling Error: Natural variability present.
• Larger sample sizes reduce error probabilities.

Example 3.5

• Different methods exhibit varying accuracy and precision.

Experiments vs. Observational Studies

• Observational Studies: Measure without influencing, show associations.
• Experiments: Impose treatments, suggest causation.
  • Use of random sampling/assignment to minimize confounding variables.

Example 3.6

• SAT prep course study: Experiment preferred to control confounding variables.

The Language of Experiments

• Experimental Units/Subjects: Individuals receiving treatments.
• Explanatory Variables/Factors: Influence response variables.

Example 3.7

• Exercise and diet study: Factors include exercise hours and diet.

Control Groups

• Can be untreated, current treatment, or placebo.

Example 3.8

• Wart treatment study: Randomized design with cryotherapy and duct tape.

Placebo Effect, Blinding, and Double-blinding

• Placebo Effect: Psychological response to perceived treatment.
• Blinding: Subjects unaware of treatment.
• Double-blinding: Neither subjects nor evaluators know treatment.

Example 3.9

• Nausea control experiment: Double-blind design with wristbands.

Matched Pairs Design

• Comparing treatments through paired subjects.

Replication and Generalizability

• Replication: Sufficient sample size for significant observations.
• Randomization: Minimizes confounding effects.

Inference and Experiments

• Statistical Significance: Results unlikely due to chance indicate other explanations.

Example 3.10

• Beverage experiment: Statistically significant differences between treatments.