Continuous outcomes are commonly compared either between different groups of participants or between linked measurements from the same participants. These designs require different analyses because they contain different sources of variability.
For independent groups, inference concerns a contrast between populations, such as a difference in mean biomarker change between Control and Drug_A. For paired measurements, inference concerns the distribution of the within-person differences, such as the change in systolic blood pressure from baseline to week 12.
The design and estimand should be specified before examining assumptions. Distributional diagnostics then assess whether a mean-based model is reasonable and, for independent groups, whether a common-variance model is credible.
5.1 Decision framework
| Design | Target | Method | Main consideration |
|---|---|---|---|
| independent groups | difference in means | Welch two-sample t-test | unequal variances allowed |
| independent groups | difference in means | pooled Student t-test | requires a common variance |
| independent groups | rank-based contrast | Wilcoxon–Mann–Whitney test | rank/distributional estimand |
| paired measurements | mean within-person difference | paired t-test | normality concerns the paired differences |
| paired measurements | rank-based paired contrast | Wilcoxon signed-rank test | interpretation depends on the distribution of differences |
Welch’s test is generally the safer mean-based procedure for independent groups because it does not require equal variances. The pooled Student test remains useful when a common-variance model is justified.