Welch (1947) proposed an adjusted t test that can be used to correct t
he serious bias in Type I error protection that is otherwise present w
hen both sample sizes and variances are unequal. The implications of t
he Welch adjustment for power of tests for the difference between two
treatments across k levels of a concomitant factor are evaluated in th
is article for k x 2 designs with unequal sample sizes and unequal var
iances. Analyses confirm that, although Type I error is uniformly cont
rolled, power of the Welch test of significance for the main effect of
treatments remains rather seriously dependent on direction of the cor
relation between unequal variances and unequal sample sizes. Neverthel
ess, considering the fact that analysis of variance is not an acceptab
le option in such cases, the Welch t test appears to have an important
role to play in the analysis of experimental data.