A. Markowski, Carol et P. Markowski, Edward, Conditions for the Effectiveness of a Preliminary Test of Variance, American statistician , 44(4), 1990, pp. 322-326
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.