Practice Observational vs Experimental Studies in Statistics

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

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Quick Recap

Observational studies gather data by watching subjects in their natural setting without any intervention, while experimental studies deliberately assign treatments to subjects and measure the outcomes. Only experiments, through random assignment, can establish cause-and-effect relationships.

Observational: Compare smokers to non-smokers (you didn't assign smoking). Experimental: Randomly assign people to take a drug or placebo (you controlled the treatment). Only experiments prove causation.

Showing a random 20 of 76 problems.

Example 1

medium
A study compares cancer rates between people living near power lines and those who don't, with no assignment of residence. Identify the study type and one confounder threatening a causal claim.

Example 2

hard
A randomized trial gives one group of patients a new drug and finds 15% recovery vs 5% in the placebo group. A skeptic asks 'How do we know the drug, not chance, caused the gap?' Answer with the design feature and the statistical tool.

Example 3

medium
A school principal compares standardized scores of students who joined an after-school program with those who didn't. The program was voluntary. Identify the study type and one alternative explanation for any score difference.

Example 4

challenge
A study reports that hospital patients given a certain therapy die more often than those not given it, concluding the therapy is harmful. Explain how this observational design could mislead even if the therapy is actually helpful.

Example 5

hard
A psychologist randomly assigns 40 students to either a meditation class or a control activity, then measures stress. After the study, several students drop out. What design feature is preserved and which is threatened?

Example 6

hard
A government compares income growth in two regions: one received a new tax credit, the other did not, with no random assignment. Researchers call this a 'natural experiment.' Is it strictly observational or experimental? Explain.

Example 7

medium
A nutrition lab feeds rats one of three diets chosen by random number table and weighs them after eight weeks. Observational or experimental, and why?

Example 8

medium
A school compares grades of students who joined a study app to those who didn't, with no assignment. Classify the study and explain why a cause-effect headline would be unjustified.

Example 9

medium
A pharmaceutical trial divides patients into treatment and placebo groups by lottery. Best label: observational, experimental, or sample survey?

Example 10

medium
Classify each: (1) randomly assigning fertilizer to plots; (2) recording which wild plants grew tallest near a river. Which is experimental?

Example 11

hard
A study finds that towns adopting a new traffic-camera program saw accidents drop 20% the next year. No towns were randomly assigned. Identify the study type and at least two threats to a causal interpretation.

Example 12

hard
Why does merely 'comparing two groups' not, by itself, make a study experimental?

Example 13

medium
Researchers find smokers have higher lung cancer rates than nonsmokers in a 20-year prospective study with no assignment. A critic says 'maybe genetics drive both.' Identify the study type and explain how a randomized trial would address the critic.

Example 14

medium
A study randomizes which restaurant a customer is sent to. Is this an experiment?

Example 15

hard
Generalization to a broader population is supported by random ____.

Example 16

medium
A double-blind experiment is one in which ____.

Example 17

easy
Random ____ of treatment is the key feature distinguishing experiments from observational studies.

Example 18

medium
A medical team wants to know if a new sleep mask improves rest. Design (A) recruits 100 people who already wear masks and 100 who don't. Design (B) randomly gives 100 people masks and withholds them from 100 others. Identify each design and which supports a causal conclusion.

Example 19

challenge
Two studies on the same question: an observational study (n=100,000) and a randomized experiment (n=500), reach opposite causal conclusions. Which should be trusted for causation and why, despite the size gap?

Example 20

easy
In which study type does the researcher actively manipulate the explanatory variable?
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