12 / 12 · Make a fair comparison
Say exactly what the result supports
Combine rates, sampling, comparison design, and uncertainty in one plain-language conclusion.
Builds on What does a small p-value actually say?
Go to practice ↓A question to keep in mind
Can '70% versus 50%' become 'this method works for everyone'?
Final fictional case: 80 volunteers are randomly assigned to two practice methods, 40 per group. Practice time and the quiz are the same. The new-method group has 28 passes; the old-method group has 20. No uncertainty interval is supplied.
State what was observed first. Then state how the comparison was made and where the conclusion stops. Random assignment helps compare the methods; volunteer recruitment does not make the participants representative of everyone.
Work through an example
| Method | Passed | Did not pass | Total |
|---|---|---|---|
| New | 28 | 12 | 40 |
| Old | 20 | 20 | 40 |
- Calculate the rates: 28/40 = 70%; 20/40 = 50%.
- Report the observed difference: 20 percentage points, or 40% relative to the old rate.
- Keep the limits: this volunteer study shows a promising difference, but its uncertainty and applicability to other learners still need examination.
Your turn
0 / 3Give the new rate, old rate, and the difference in percentage points.
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- New rate: 70 %
- Old rate: 50 %
- Difference: 20 points
70% versus 50% is a 20-percentage-point observed difference. These numbers describe the groups in this study.
Which statements are given by the case, and which need more evidence?
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- The new group's observed pass rate is 70%. → Given or calculated from the case
- The two groups were randomly assigned. → Given or calculated from the case
- Every kind of learner will benefit. → Needs more evidence
- The true improvement is exactly 20 percentage points. → Needs more evidence
The counts and assignment are given. Universal benefit and an exact population effect go beyond the case.
Which conclusion is the most careful without dismissing the result?
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In this randomized volunteer study, the new group had a higher observed pass rate. Check uncertainty and repeat in other learner groups before generalizing.
A useful conclusion names the observed result, how it was obtained, and its limits. That is the habit this course aims to build.
Bring it back to your own work
Write a three-sentence result note: what was measured, how people were selected or assigned, and what remains uncertain. Use this case or your own clearly labeled fictional example.
Statistical literacy: directory, audit and transfer assessment
How do I retain independent judgment when using AI here?
Keep your own answer before consulting an AI candidate. Check sources, calculations, inference and conditions; explain adoption or rejection. Then solve a new-context task independently and apply the checks to this lesson.
Practice the verification workflow and keep a recordMy learning status
Mark statuses manually; visits do not establish mastery. Languages share statuses while lessons keep their own answers. This backup contains statuses only, not answers or notes.