What t-test to use: Student’s or Welch’s?

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

Our hypothesis test

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Test assumptions

Assumptions	Student’s t-test	Welch’s t-test
Two independent, random samples
The two populations have Normal distributions
The variances of the two populations are equal

Sample size consideration

If the sample sizes are unequal between the two groups, Welch's t-test performs better than Student's t-test.

What test to use?

Performing the test in Genstat

Performing a Student’s t-test or Welch’s t-test in Genstat is straightforward. 

From the menu bar, select Stats | Statistical tests | One- and two-sample t-tests. Then, in the T-Tests menu, set the type of test to Two-sample.

Running a Student’s t-test in Genstat

We can run a Student’s t-test by clicking the Options button, then selecting Pooled as the method used to estimate the variances for the test. 

Running a Welch’s t-test in Genstat

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