Robustness of the Analysis of Variance, the Welch Procedure and a Box Procedure to Heterogeneous Variances

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Abstract
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 α 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.