AP® Statistics review sheet from Aim for Five (aimforfive.com/stats/units/1/1-10)
Unit 1 · Topic 1.10
1.10 The Investigative Question Revisited and Data Collection
This topic connects the investigative question to how data are collected. You'll sharpen the question so it points to the variables, the analysis and the conclusion, then tell apart a census, an observational study and an experiment, and decide how far the results can be generalized.
Key terms
- census
- observational study
- experiment
- explanatory and response variables
- confounding variable
- generalizing to a population
Three jobs of an investigative question
A fully built investigative question does three things:
- It names the variable or variables you'll collect, so it tells you what to measure.
- It points to the analysis. If you plan a significance test, it names the parameter and the direction you're looking for (greater than, less than, different from, or an association). If you plan a confidence interval, it names the parameter you want to estimate.
- It says what kind of conclusion is possible: which population the result applies to and, for an experiment with random assignment, whether a cause-and-effect claim is allowed.
Census, observational study, experiment
A census collects data from every member of the population. No estimating is needed, but it's rarely practical.
An observational study records variables without changing anything. Researchers watch, measure or ask. A survey, which asks people a standard set of questions, is one kind. A prospective study picks its units now and follows them into the future. A retrospective study picks its units now and looks back at their past.
An experiment deliberately assigns treatments to experimental units, then measures a response. The experimental units are the units that receive treatments; when they're people they're called subjects or participants. The explanatory variable (factor) is what the researcher changes, its levels are the treatments, and the response variable is the outcome measured afterward. With two factors, each combination of levels is a treatment.
Confounding
A confounding variable is linked to both the explanatory variable and the response, so it offers another explanation for the relationship you see. Example: students who eat breakfast have higher grades. Family income could be confounding, since it may relate to both eating breakfast and grades.
Observational studies can't rule out confounding, so they can show association but not cause and effect. Random assignment in an experiment spreads confounding variables evenly across groups, which is why experiments can support causal claims.
How far can you generalize?
Two separate questions decide what you can conclude:
| How units were chosen | Random assignment? | Conclusion allowed |
|---|---|---|
| Random sample | Yes | Cause and effect, for the whole population |
| Random sample | No | Association only, for the whole population |
| Not random (volunteers, convenience) | Yes | Cause and effect, only for units like those studied |
| Not random (volunteers, convenience) | No | Association only, only for units like those studied |
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Identify the study type and conclusion
Researchers recruit 200 adult volunteers. They randomly assign 100 to walk 30 minutes a day and 100 to keep their usual routine. After 8 weeks, the walking group's mean resting heart rate dropped more. Is this an experiment or an observational study? What conclusion is justified, and for whom?
Show the solutionHide the solution
- Step 1: Researchers assigned the treatments (walking vs. usual routine), so it's an experiment. Explanatory variable: walking routine; response: change in resting heart rate.
- Step 2: Treatments were randomly assigned, so a cause-and-effect conclusion is reasonable.
- Step 3: The subjects were volunteers, not a random sample, so the result applies only to adults similar to these volunteers.
Answer: Experiment. Because of random assignment, walking caused the larger drop in heart rate, but only for adults like those who volunteered, since they weren't randomly selected.
- Example 2Calculator allowed
Trap: causation from an observational study
A random sample of 1,500 teens finds that those who play video games more than 3 hours a day have lower grades on average. A headline says, "Gaming lowers grades." Evaluate the headline and name a possible confounding variable.
Show the solutionHide the solution
- Step 1: No treatments were assigned; the researchers just recorded gaming time and grades. It's an observational study.
- Step 2: Observational studies show association, not cause and effect.
- Step 3: Possible confounder: time spent on homework. Teens who game more may spend less time on homework, and less homework is linked to lower grades.
- Step 4: The random sample does let you generalize the association to the population of teens it was drawn from.
Answer: The headline overreaches. This observational study shows heavy gaming is associated with lower grades among teens, but a confounding variable such as homework time could explain it.
Common mistakes
- Calling a study an experiment just because it has two groups. If the researcher didn't assign the groups, it's observational.
- Mixing up the two kinds of randomness: random sampling lets you generalize; random assignment lets you claim cause and effect.
- Naming a confounding variable without explaining how it's linked to both the explanatory and response variables.
On the exam
- Free-response design questions often ask whether a conclusion is justified. Address both scope questions: who it applies to (random sample?) and whether it's causal (random assignment?).
- When you name a confounding variable, describe its connection to both variables in context. Just naming it usually isn't enough.
Connected topics
Videos
Check yourself
4 questions on 1.10 The Investigative Question Revisited and Data Collection. Pick an answer to see if you got it, and why.
Which of the following is a census?
Researchers want to know whether a new reading app improves vocabulary. Which plan is an experiment?
An observational study finds that people who own a dog tend to have lower blood pressure than people who don't. Which of the following is the best example of a possible confounding variable?
A study investigates whether the amount of time teens spend on social media is related to how many hours they sleep. In this study, which is the response variable?
0 of 4 answered