Testing Complex a Priori Contrasts on Means from Independent Samples

The robustness of the t statistic on complex contrasts, ψ, using MS_W in the estimate of s_ψ is compared with that of t”, a statistic derived by Welch (1947). The t statistic is robust to violations of the homogeneity of variance assumption only if n's are equal and all weights have the same absolute value. The Welch t” is robust for all combinations explored with any set of weights and either equal or unequal n's. Since heterogeneous variances are often encountered in behavioral experiments, the Welch t” is recommended as the benchmark test for complex contrasts.