Compare Overall and Grouped Rates

See how group composition can reverse an apparent comparison.

All worksheets

5 questions0m 0s

Learn the skill

Calculate rates within comparable groups before combining them. Overall rates weight groups by their sizes. Different group mixes can reverse a ranking, and observational rates alone do not establish causation.

Worked example

A program serving mostly beginners and one serving mostly advanced learners may have different overall success rates even when their within-group patterns tell another story.

Invented Program Results

Program A: beginners 9 successes out of 10; advanced learners 12 out of 30. Program B: beginners 24 successes out of 30; advanced learners 3 out of 10. Learners were not randomly assigned. These are fictional data.

1. What is Program A's beginner success rate? 80% 90% 40%

2. Which program has the higher advanced-group success rate? Program A Program B They are equal

3. Which program has the higher overall success rate? Program A They are equal Program B

4. What helps explain the reversal? The denominators are irrelevant The programs have different mixes of beginner and advanced learners Arithmetic cannot compare groups

5. Do these observational results prove one program caused better outcomes? No, assignment and other differences need consideration Yes, all rate differences are causal Yes, any larger total proves causation

Review your work

0correct

Complete the questions to review each answer.

View dashboard