Practice Control Group in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A control group is the comparison group in an experiment that does not receive the main treatment being tested. It provides a baseline for deciding whether the treatment changes the outcome.
You cannot tell whether a treatment had an effect unless you know what would have happened without it. The control group gives you that comparison point.
Showing a random 20 of 50 problems.
Example 1
easyTrue or false: A control group must be identical in size to the treatment group.
Example 2
mediumWhy does pairing a control group with random assignment give stronger evidence than a control group chosen by the researcher?
Example 3
challengeAn experiment measures cancer-cell death rate. Treatment: 80% death. Control (untreated cells): 5% death. Why is reporting the absolute difference ( percentage points) more honest than reporting 'treatment kills 16x more cells'?
Example 4
mediumDescribe what a 'positive control' is and give an example.
Example 5
easyIn medical trials, the control group is often given a placebo instead of nothing. Why use a placebo rather than nothing?
Example 6
mediumA diet study has a treatment group and a control group, but the control group is given a different, untested diet rather than their normal diet. Why does this weaken the control, and what is the fix?
Example 7
mediumTwo designs: (A) treatment vs placebo control, (B) treatment vs a group on a totally different unrelated drug. Which has a valid control group for testing the treatment?
Example 8
easyWhy can't you tell whether a treatment worked if there is no control group?
Example 9
easyA new shampoo is tested by giving it to every participant — no comparison group. What is missing?
Example 10
mediumA treatment group improved 12 points and the control group improved 12 points. State the estimated treatment effect and what the equal improvement implies.
Example 11
mediumA pilot study finds the treatment group's mean blood pressure dropped 15 mmHg; the control group's mean dropped 12 mmHg. What is the estimated treatment effect?
Example 12
mediumA study's control group quietly started taking the treatment on their own (contamination). Explain how this weakens the control group's usefulness.
Example 13
easyIn an experiment, the group that receives the actual treatment being tested is called the what?
Example 14
easyAn 'active control' group receives an existing standard treatment rather than nothing. Why might researchers use an active control instead of a placebo?
Example 15
challengeA study has a placebo control AND random assignment but the doctors knew who got the real drug and rated outcomes more favorably for them. The control exists, so why are the results still biased?
Example 16
mediumAn ad-platform A/B test sends the new ad to one group and nothing to a randomly held-out group. The held-out group functions as what?
Example 17
easyA study reports the treatment group had a 60% recovery rate. Why is this number uninformative without the control group's rate?
Example 18
easyFill in the blank: A control group should be _____ to the treatment group in every way except the treatment.
Example 19
mediumA fitness study compares people who joined a new gym to people who didn't join any gym. What's wrong with using non-joiners as the control group?
Example 20
hardAn ed-tech company runs an A/B test where the 'control' group gets the OLD app and the 'treatment' group gets the NEW app. The new app loads slower in week 1 due to bugs. What does the control group enable here?