Practice Observational vs Experimental Studies in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

An observational study records data without imposing treatments, while an experiment deliberately manipulates a variable. Only experiments with random assignment can establish causation; observational studies can only show association.

Observational: you watch people who already smoke and compare their lung cancer rates to non-smokers. Experimental: you randomly assign people to smoke or not (unethical, but illustrates the point). The observational study might find that smokers differ from non-smokers in many ways (diet, exercise, stress)โ€”so you can't be sure smoking caused the cancer. The experiment controls for everything else.

Showing a random 20 of 50 problems.

Example 1

challenge
A newspaper headline reads 'People who eat breakfast weigh less.' Design an experiment that could test causation, naming the key feature that observation lacks.

Example 2

easy
True or false: only experiments can establish causation.

Example 3

hard
Why is it impossible to conduct a fully randomized experiment to test the effect of poverty on health outcomes? What study design limitations result from this constraint?

Example 4

hard
What is Simpson's paradox?

Example 5

easy
True or false: experiments are always the better choice regardless of ethics or practicality.

Example 6

medium
Why is it unethical to randomly assign children to a smoking group to study health effects?

Example 7

medium
Classify: a prospective study that follows a cohort over time, recording but not assigning their exposures.

Example 8

easy
A study records the diets of people who already chose to eat them and tracks health, imposing no treatment. Observational or experimental?

Example 9

challenge
Smoking-cancer causation was established largely from observational data. Explain how scientists strengthened a causal case without a randomized human experiment.

Example 10

medium
True or false: a placebo group is a feature of observational studies.

Example 11

hard
A 1980s study found people who took vitamin E supplements had lower heart disease rates. Later randomized trials found NO effect. Explain the discrepancy.

Example 12

easy
A survey asks 200 people how many hours of sleep they got and their stress level. Type?

Example 13

medium
What is a 'natural experiment'?

Example 14

hard
A study finds a strong correlation between ice cream sales and drownings. Why can't we conclude ice cream causes drowning?

Example 15

easy
True or false: assigning subjects to groups by chance makes a study experimental.

Example 16

medium
A health agency cannot ethically assign people to smoke. What study type must it use, and what is the cost?

Example 17

easy
Researchers randomly assign patients to a new drug or placebo and compare. Observational or experimental?

Example 18

easy
A confounding variable in an observational study is best described as what?

Example 19

easy
Observational studies can only establish ____.

Example 20

hard
Why is a randomized controlled trial (RCT) considered the 'gold standard' for testing medical treatments?