Control Group Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Control Group.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept 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.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: Control Group checks whether the study design supports a fair comparison before interpreting the outcome.

Common stuck point: Students often know a procedure related to control group but skip the recognition step: Did the study use a design feature that makes the groups comparable before the outcome is measured? That leads to a calculation or graph that looks reasonable but answers a different question.

Sense of Study hint: Ask: Did the study use a design feature that makes the groups comparable before the outcome is measured?

Worked Examples

Example 1

medium
A 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?

Answer

3 mmHg3 \text{ mmHg}

First step

1
Treatment effect = treatment change − control change.

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Example 2

medium
Describe what a 'positive control' is and give an example.

Example 3

medium
A new fertilizer is tested. Plot A gets fertilizer, plot B in a different field gets none. Identify why plot B is a poor control.

Example 4

hard
A trial reports a 20%20\% improvement in the treatment group. A skeptic asks, 'What did the control group do?' Why is this the right question?

Example 5

hard
Why is a control group of zero subjects (no comparison) almost always worse than a control of just 10 subjects?

Example 6

hard
A study uses 'sham surgery' as the control for a real surgery. Why is the sham control especially important here?

Example 7

challenge
An experiment measures cancer-cell death rate. Treatment: 80% death. Control (untreated cells): 5% death. Why is reporting the absolute difference (7575 percentage points) more honest than reporting 'treatment kills 16x more cells'?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
In a drug trial, the group that receives no active drug to provide a baseline is called the what?

Example 2

easy
Why can't you tell whether a treatment worked if there is no control group?

Example 3

easy
In an experiment, the group that receives the actual treatment being tested is called the what?

Example 4

easy
A skincare test applies cream to one group and nothing to a comparable group. Which is the control group?

Example 5

easy
For a control group to be useful, it should be what relative to the treatment group (besides not getting treatment)?

Example 6

easy
A gardener compares fertilized plants to plants grown in a totally different climate. Why is the second group a poor control?

Example 7

easy
A clinic gives all patients a new therapy and reports they improved, with no comparison group. What essential element is missing?

Example 8

easy
In medical trials, the control group is often given a placebo instead of nothing. Why use a placebo rather than nothing?

Example 9

medium
A study gives a tutoring program to motivated volunteers and uses uninterested non-volunteers as the control. Why is this control group flawed?

Example 10

medium
A trial reports the treatment group improved 30%. The control group also improved 25%. What is the estimated treatment effect, and why does the control matter here?

Example 11

medium
Without a control group, a sunscreen study claims '90% of users avoided sunburn.' Give two non-treatment explanations a control could rule out.

Example 12

medium
Two 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 13

medium
In an A/B website test, version A (current) and version B (new) both get random visitors. Which serves as the control, and what does comparing them reveal?

Example 14

medium
A study's control group quietly started taking the treatment on their own (contamination). Explain how this weakens the control group's usefulness.

Example 15

medium
Why does pairing a control group with random assignment give stronger evidence than a control group chosen by the researcher?

Example 16

challenge
A trial finds treatment and control both improved a lot, with no significant difference. A reporter says 'the treatment clearly works because patients improved.' Use the control group to refute this.

Example 17

challenge
Explain why a 'historical control' (comparing new patients to past patients treated years ago) is generally weaker than a concurrent randomized control group.

Example 18

challenge
A 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 19

medium
A 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 20

medium
A treatment group improved 12 points and the control group improved 12 points. State the estimated treatment effect and what the equal improvement implies.

Example 21

easy
In an experiment, what is the main purpose of the control group?

Example 22

easy
An experimenter tests a sleep aid by giving everyone the pill on Monday and asking how they slept by Friday. Without a control group, what alternative explanation can't be ruled out?

Example 23

easy
In a vaccine trial, the group given saline injections instead of the vaccine is called what?

Example 24

easy
An 'active control' group receives an existing standard treatment rather than nothing. Why might researchers use an active control instead of a placebo?

Example 25

easy
A study reports the treatment group had a 60% recovery rate. Why is this number uninformative without the control group's rate?

Example 26

medium
A study uses 'historical controls' — patients treated last year as the comparison group. List one weakness of this design.

Example 27

medium
A 'wait-list control' receives the treatment after the study ends. What threat does this control address?

Example 28

medium
A researcher uses a 'negative control' — a treatment expected to have NO effect. What does this control reveal?

Example 29

medium
A 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 30

medium
A trial has treatment group with mean change +10+10 units and control with mean change +8+8 units. Without further info, is the treatment effective?

Example 31

medium
A double-blind study uses a control group. What does 'double-blind' add that the control group alone doesn't?

Example 32

medium
An 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 33

medium
Some studies use 'matched controls' — each treatment subject paired with a similar control. What's the main motivation?

Example 34

hard
Why might a study include both a placebo control and an active control?

Example 35

hard
An 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?

Example 36

hard
A nutrition study uses 'each participant is their own control': measure them on a normal diet, then on a new diet. What confounder remains?

Example 37

hard
A school superintendent points to a single high-performing school adopting a new method and concludes the method works. Why is the absence of a control problematic?

Example 38

hard
A school decides to skip the control group because 'denying students a useful program is unethical.' Suggest an ethical design that still includes a control group.

Example 39

challenge
A controversial drug trial uses no control because 'all early-stage cancer patients should get the treatment.' A regulator argues this design CAN'T prove the drug works. Why is the regulator correct?
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Background Knowledge

These ideas may be useful before you work through the harder examples.

experimental designrandom assignment