Student’s t-test or Welch’s t-test?

C. Supakorn


Imagine we are interested in whether female undergraduate students with blonde or brown hair are different heights, on average. To investigate this, we randomly select 50 blonde and 50 brown haired female undergraduate students and measure their height.


Unequal sample variances and/or unequal sample sizes

→ Welch’s t-test[1] (also known as the unequal variances t-test) performs better than Student’s t-test

Equal population variances and equal sample sizes

→ Student’s t-test has more power than Welch’s t-test



Performing a Student’s t-test or Welch’s t-test in Genstat is easy. In the menu bar, select Stats | Statistical tests | One- and two-sample t-tests… and then, in the T-Tests menu, set the type of test to “Two-sample”.






Running a Welch’s t-test in Genstat


We can run a Welch’s t-test by clicking the Options button and then checking “Separate” as the method used to estimate the variances for the test.







Running a Student’s t-test in Genstat


To run a Student’s t-test, in the T-Test Options menu select “Pooled” as the method used to estimate the variances for the test.






[1] Welch, B. L. (1947). “The generalization of “Student’s” problem when several different population variances are involved”. Biometrika. 34 (1–2): 28–35.