Welch's t-test
Compares the mean of a measurement between two independent groups, without assuming both groups have the same spread.
Clinical example
Two treatment arms in a trial, and you want to know whether mean systolic blood pressure at 12 weeks differs between them. One measurement per patient, two separate groups of patients.
When to use it
- The outcome is a measurement on a continuous scale.
- You compare exactly two groups, and each patient is in only one of them.
- You don't need to adjust for baseline values or confounders.
Assumptions to check
Independent observations
One value per patient. Repeated measurements or clustered patients need a mixed model.
Equal variances not needed
That's the point of Welch's version. Skip the variance test beforehand.
What to report
- Mean per group with SD
- Mean difference with 95% CI
- The exact p-value, not just "p < 0.05"
Common mistakes
Don't run many separate tests
Testing every pair of groups, outcome or time point separately piles up false positives. Use one model, prespecify the main comparison, and correct for multiple comparisons where needed.
Paired data need a paired test
Measurements in the same patient are related. An unpaired test ignores that and loses power, or gives the wrong answer.
Report the effect, not just the p-value
Give the estimate (difference, ratio) with its 95% confidence interval and the exact p-value.
Alternatives
| If your situation is… | Use |
|---|---|
| Strongly skewed data, small groups | Mann-Whitney U test |
| Same patients measured twice | Paired t-test |
| Baseline value measured too | ANCOVA (adjusting for baseline) |
| Three or more groups | One-way ANOVA |
In your software
# R (Welch is the default)
t.test(sbp_12wk ~ arm, data = trial)
T-TEST GROUPS=arm(1 2)
/VARIABLES=sbp_12wk
/CRITERIA=CI(.95).