Conditions for the Effectiveness of a Preliminary Test of Variance

We evaluate the performance of the F test for the equality of two variances as a preliminary test to determine the appropriateness of the two-sample t test. When sampling is from a normal distribution, our results indicate that, for equal sample sizes, the t test is insensitive to variance heterogeneity and hence no preliminary test is necessary. For unequal sample sizes, the F test has small probability of detecting many alternatives for which the t test performs poorly, and so the F test is not an effective preliminary test. When sampling is from other distributions, our results confirm the sensitivity of the F test to the normality assumption.