Short on time? This page is the recap. For explanations and worked examples, use the full study guide.
Recap
- A full investigative question has three components. It names the variables to collect, shows the analysis, and states what can be concluded about which population.
- For analysis, the question either asks to estimate a parameter with a range of plausible values, or to test a claim about a parameter in a stated direction: different from, greater than, less than, or an association (not independent).
- A census records every individual in the population. A sample records only some.
- In an observational study nothing is imposed; values are recorded. In an experiment the researcher assigns treatments, then measures a response.
Key relationships
| Term | Meaning |
|---|---|
| Prospective study | Units chosen now; data recorded now and into the future |
| Retrospective study | Units chosen now; data from the past gathered |
| Survey | Standard questions asked of people (observational) |
| Experimental unit | What a treatment is given to; people are subjects or participants |
| Factor (explanatory variable) | Variable whose levels are imposed |
| Treatment | One level, or one combination of levels across factors |
| Number of treatments | Product of the numbers of levels (3 levels × 2 levels = 6) |
| Response variable | Outcome measured on each unit after the treatment |
| Confounding variable | Associated with both explanatory and response; gives another explanation |
| Random selection | Generalise to the whole population sampled |
| Not random (chosen or volunteers) | Generalise only to individuals like those in the study |
| Random assignment (experiment) | Allows a cause-and-effect conclusion |
Assumptions and conventions
- “Random” means a random mechanism, such as a random number generator, chose every unit. Choosing “at will” is not random.
- A census is about who is measured; observational versus experiment is about how the data arise.
- Confidence intervals and hypothesis tests come later. Here you only identify which one a question calls for.
Mistakes to avoid
- Calling any two-group comparison an experiment. Ask: were the treatments imposed?
- Adding levels to count treatments. Multiply them.
- Mixing up units and treatments. Units receive treatments.
- Naming a confounder linked to only one variable. Show both links, in context.
- Generalising from volunteers to a whole population, however many there are.
- Claiming cause and effect from an observational study, even a random one.
- Writing a question with no population or no clear parameter and direction.
Quick self-check
- A study gives 4 diets and 2 exercise plans to 80 volunteers. How many treatments? (4 × 2 = 8)
- A hospital chooses 500 patients today and checks their past records for smoking. What type of study? (Observational, retrospective)
- A random sample of a town’s adults is surveyed. Can results be generalised to the town? Can they show cause and effect? (Yes, to the town’s adults; no, it is observational)
Next: practice questions.