Paired Data Versus Two Independent Samples
To estimate the mean improvement in test scores for 30 students after a review session, a teacher constructs separate confidence intervals for the mean pre-test and post-test scores. The teacher then estimates the improvement by subtracting these two intervals. What is the primary flaw in this method, and what is the correct statistical procedure?
| Student | Pre-test Score | Post-test Score |
|---|---|---|
| 1 | 68 | 75 |
| 2 | 70 | 78 |
| … | … | … |
The mistake is in using a t-distribution; a z-distribution should be used when sample sizes are large.
There is no mistake; subtracting the independent confidence intervals yields the correct confidence interval for improvement.
The mistake is treating paired data as if they were from independent samples; the proper approach is to compute the difference for each student and perform a one-sample t-interval on these differences.
The error is in calculating means instead of medians; paired data should be analyzed using medians.
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