Practice Random Assignment in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Random assignment is the process of placing participants into treatment groups by chance. It helps make the groups similar at the start of an experiment so differences at the end are more likely to be caused by the treatment.
Random sampling helps you generalize to a population. Random assignment helps you compare treatments fairly inside an experiment.
Showing a random 20 of 50 problems.
Example 1
challengeDistinguish precisely the inferential roles: a study uses random sampling but not random assignment; another uses random assignment but not random sampling. What can each validly claim?
Example 2
easyDoes random assignment guarantee the groups are exactly identical in every trait?
Example 3
challengeExplain why a study can have random assignment but still show a biased estimate of treatment effect if the outcome is measured non-blindly.
Example 4
easyRandom assignment supports a claim of what kind of relationship between treatment and outcome?
Example 5
challengeA researcher claims that because she randomly assigned treatment, her results automatically generalize to the whole country. Explain the flaw and which random procedure generalization actually requires.
Example 6
easyDoes random assignment require that each subject have an equal probability of being in each treatment group?
Example 7
easyWhich requires random assignment: generalizing a poll to all voters, or claiming a drug caused recovery?
Example 8
mediumIf a researcher has used random assignment, what type of confounders has it balanced: only the ones they measured, or also unknown ones?
Example 9
easyA researcher draws names from a hat to decide who gets the new training program and who doesn't. What design feature is this?
Example 10
easyAfter randomly assigning subjects, a researcher swaps a few people between groups to 'balance ages.' Did she preserve random assignment?
Example 11
hardA 'natural experiment' uses random or quasi-random variation in policy (e.g., a lottery for school admission). Why is this nearly as good as a designed experiment?
Example 12
mediumA trial randomly assigns 1,000 patients to drug or placebo. The drug group ends up with slightly more men (53% vs 47%). Does this break random assignment?
Example 13
easyWhy does random assignment let us attribute outcome differences to the treatment?
Example 14
hardA researcher claims their study has both random sampling and random assignment. What two distinct guarantees does this dual structure provide?
Example 15
mediumIn a randomized experiment with , the researcher finds the treatment group is sicker at baseline. Was random assignment misapplied?
Example 16
hardAn online experiment randomly assigns 50,000 users to two versions of a webpage. After running, the data scientist sees the treatment version has more late-night users. What likely explains this?
Example 17
mediumTwo designs: (A) randomly assign smokers and nonsmokers to groups for an unrelated drug; (B) compare smokers vs nonsmokers for lung effects. Which uses random assignment, and which can claim causation about smoking?
Example 18
mediumA trial randomly assigns 200 patients to drug or placebo. Critics say age wasn't balanced perfectly. Is this a fatal flaw of random assignment? Explain.
Example 19
mediumRandom assignment is sometimes impossible — for example, you can't randomly assign people to smoke for 20 years. What kind of study fills this gap, and what is its limitation?
Example 20
mediumWhy do large experiments rely on random assignment rather than carefully matching subjects on every known variable?