Numerous studies have documented the robustness of t and F to heterogeneous variances under the restricted condition of equal n's. Likewise, the distortion of 01. in the presence of unequal n's and variances has been demonstrated in both mathematical and empirical studies. Several investigations, however, have shown the Welch technique to be robust to this disturbing situation in the two group case. The present study was addressed to the k group AOV situation. Monte Carlo methods were employed to contrast several procedures with respect to a.) control over Type I errors and b.) power. Results indicate that the generalized Welch technique may be substituted for the AOV when variances are heterogenEous and n's are unequal.A TEST OF THE null hypothesis, H 0 : fJ. 1 =fJ. 2 = ... (J.k is generally conducted through analysis of variance (AOV) procedures. With K independent samples, the derivation assumes that the population variances are equal. In practice, however, the condition of homogeneous variances cannot always bernet. The effect of heterogeneous variances on the probability of a Type I error has been the subject ofboth J:IRthematical and empirical studies. As the review below will demonstrate, the effect of heterogeneous variances is generally not serious when n's are equal and of reasonable size, but when n's are unequal protection against Type I errors rapidly deteriorates.

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The robustness of the t statistic on complex contrasts, ty, using MS in the estimate of s. 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 11 is robust for all combinations explored with any set of weights and either equal or unequal n f s. Since heterogeneous variances are often encountered in behavioral experiments, the Welch t" is recommended as the benchmark test for complex contrasts.at Yale University Library on July 23, 2015 http://jebs.aera.net Downloaded from 208 (1966, pp. 337-345). K Let lii. be defined as Ew. t u. where w. is a vector of K K weights such that Ew = 0. Then i|i, = Ew,, Y is an unbiased estimate of I|J. that is normally distributed if the Y 's are normally distributed or the n f s are reasonably large. To test the null hypothesis, Ho: ty. = 0^ we may construct the statistic t defined as: KoJw and Games Behavioral examples of usage on a single factor are found in Games (1971) and Tjosvold (1977). Examples using an interaction contrast in a two-factor design are found in Myers

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