Practice Experimental Design in Statistics

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

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Quick Recap

Experimental design is the careful planning of experiments to establish cause-and-effect relationships by controlling variables, using comparison groups, and randomly assigning subjects to treatment and control conditions to isolate the effect of interest.

Want to know if a new fertilizer helps plants grow? You can't just use it on some plants and see if they grow - maybe they would've grown anyway! You need identical plants, give fertilizer to some (treatment) but not others (control), and keep everything else the same.

Showing a random 20 of 76 problems.

Example 1

medium
Two factors in a factorial design: drug (A vs B) and dose (low vs high). How many treatment combinations are there?

Example 2

easy
In a fertilizer experiment, which group receives no fertilizer to serve as a baseline?

Example 3

hard
An effect detected only in one subgroup (e.g., women) but not overall is called a ___ effect.

Example 4

hard
A study with 2020 subjects per group finds a small, non-significant difference between treatment and control. A larger replication with 20002000 per group finds the same small difference, but now significant. What does this say about sample size and effect detection?

Example 5

challenge
A company runs an experiment to test a website change but only randomizes by day (treatment on odd days, control on even days). Why is this design weaker than randomizing visitors, and identify one confounder it cannot control.

Example 6

easy
A farmer wants to test whether a new fertiliser improves crop yield. She applies the new fertiliser to Field A and uses the old fertiliser on Field B. She finds Field A produces more. Can she conclude the new fertiliser is better? Identify the flaw in the experiment.

Example 7

challenge
A randomized trial finds treatment reduces symptoms by 20% (p=0.03p=0.03). Skeptics argue the result is due to chance, bias, or confounding. Address each.

Example 8

medium
A study compares two diets in 60 subjects. With random assignment, what kind of inference is supported by a statistically significant difference?

Example 9

easy
What word describes when neither the patients nor the doctors know who received the drug or the placebo?

Example 10

challenge
A randomized trial finds that on average the treatment group did better. A critic notes that the trial only included healthy young adults. What concept limits generalizing the result to all patients?

Example 11

medium
A doctor tests a new headache medicine. She gives the medicine to patients who ask for it and compares their recovery to patients who didn't ask. Identify at least two problems with this experimental design.

Example 12

medium
An experiment tests a teaching method but gives it to morning classes and uses afternoon classes as control. What variable is confounded with method?

Example 13

easy
A gardener gives fertilizer to half her identical plants (treatment) and nothing to the other half (control), then compares growth. Is this an experiment?

Example 14

hard
A drug trial randomizes patients but some in the treatment arm refuse the drug and switch to placebo. Why is 'intention-to-treat' analysis the standard, not 'as-treated'?

Example 15

hard
A teacher wants to compare two reading programs in her 44 classes. Why is randomly assigning programs to classes (rather than to individual students) limited as a causal study?

Example 16

medium
A study randomly assigns 100 students to a tutoring group and 100 to no tutoring, but the tutoring group also happens to get free lunch. Identify the threat and how to fix the design.

Example 17

medium
A study finds that students who get more sleep get higher grades. Why can't we conclude that sleep CAUSES higher grades from this study?

Example 18

medium
A researcher tests three doses (low, medium, high) of a fertilizer on 6060 identical plants. List one valid randomization scheme.

Example 19

hard
A within-subject crossover trial assigns each subject to both treatments in random order. Why is this typically more powerful than a parallel-group design with the same nn?

Example 20

medium
A study assigns the first 50 patients to treatment and the next 50 to control. Why is this design flawed?
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