Exact Type 1 Error Rates for Robustness of Student's t Test with Unequal Variances

Abstract

It is noted that disagreements have arisen in the literature about the robustness of the t test in normal populations with unequal variances. Hsu's procedure is applied to determine exact Type I error rates for t. Employing fairly liberal but objective standards for assessing robustness, it is shown that the t test is not always robust to the assumption of equal population variances even when sample sizes are equal. Several guidelines are suggested including the point that to apply t at α = .05 without regard for unequal variances would require equal sample sizes of at least 15 by one of the standards considered. In many cases, especially those with unequal N's, an alternative such as Welch's procedure is recommended.