Chapter 5 Comparing Two Groups 157 A natural way of trying to salvage homoscedastic methods is to test for equal variances, and if not significant, assume the variances are equal. Even under normality, this strategy can fail because tests for equal variances might not have enough power to detect unequal variances in situations where the assumption should be abandoned, even when the test for equal variances is performed at the 0.25 level (e.g., Hayes & Cai, 2007; Markowski & Markowski, 1990; Moser, Stevens, & Watts, 1989; Wilcox, Charlin, & Thompson, 1986; Zimmerman, 2004). 5.3 Comparing Medians and Other Trimmed Means This section considers the problem of testing H 0 : µ t1 = µ t2 , the hypothesis that two independent groups have equal trimmed means, plus the related goal of computing a 1 - confidence interval for µ t1 - µ t2 . Included as a special case is a method for comparing medians, which requires specialized techniques.