AP Statistics 3.1 Introducing Statistics: Do the Data We Collected Tell the Truth? Study Notes
AP Statistics 3.1 Introducing Statistics: Do the Data We Collected Tell the Truth? Study Notes- New syllabus
AP Statistics 3.1 Introducing Statistics: Do the Data We Collected Tell the Truth? Study Notes -As per latest AP Statistics Syllabus.
LEARNING OBJECTIVE
- Given that variation may be random or not, conclusions are uncertain.
Key Concepts:
- Introducing Statistics: Do the Data We Collected Tell the Truth?
Introducing Statistics: Do the Data We Collected Tell the Truth?
Introducing Statistics: Do the Data We Collected Tell the Truth?
Statistical conclusions are only as reliable as the data collection process. If data are collected in ways that do not involve chance (e.g., convenience samples, voluntary response), the results are likely biased and untrustworthy.
Guiding Questions About Data Collection Methods:
- Was random selection used? (ensures representativeness of the population)
- Was random assignment used? (in experiments, ensures groups are comparable)
- Could bias be introduced through:
- Sampling method (convenience, voluntary response)?
- Question wording (leading or confusing questions)?
- Nonresponse (certain groups not participating)?
- Measurement error (inaccurate recording)?
- Are the conclusions generalizable to the larger population?
Trustworthy vs Untrustworthy Methods
| Trustworthy (uses chance) | Untrustworthy (does not use chance) |
|---|---|
| Simple Random Sample (SRS) | Convenience Sample |
| Stratified Random Sample | Voluntary Response Sample |
| Cluster or Systematic Sampling (if random) | Self-selected or opt-in survey |
| Random Assignment in Experiments | Nonrandom Group Assignment |
Note: Only methods relying on chance (random selection or random assignment) allow us to trust the conclusions.
Example
A school newspaper wants to estimate the average number of hours students spend on homework each week. They ask readers to respond to an online survey. 200 students respond.
Is this method of data collection trustworthy? Why or why not?
▶️ Answer / Explanation
Step 1 — identify the method: This is a voluntary response sample because only students who chose to respond are included.
Step 2 — evaluate: Voluntary response samples are typically biased because students with stronger opinions (e.g., very busy or very free) are more likely to respond.
Step 3 — conclusion: The data collection method does not rely on chance, so the results are not trustworthy and cannot be generalized to the whole school.
Example
A student council member wants to know if students prefer pizza or burgers in the cafeteria. She asks the first 50 students in the lunch line on Monday.
Is this sample method trustworthy? Why or why not?
▶️ Answer / Explanation
Step 1 — identify the method: This is a convenience sample because only students in the lunch line at that time are surveyed.
Step 2 — evaluate: Students who eat early lunch on Monday may not represent the whole school (different grade levels, activities, or preferences).
Step 3 — conclusion: The method does not involve chance, so the conclusions are biased and untrustworthy.
Example
A teacher wants to test if background music improves math test performance. She lets students choose whether they want music or silence during the test.
Is this experimental design trustworthy? Why or why not?
▶️ Answer / Explanation
Step 1 — identify the design: This experiment uses nonrandom assignment because students chose their own groups.
Step 2 — evaluate: Students who pick music may differ systematically from those who do not (e.g., study habits, test anxiety). This introduces confounding variables.
Step 3 — conclusion: Without random assignment, the experiment is not trustworthy for establishing cause-and-effect.