372: The Anova and Multiple Comparisons for Data with Heterogeneous Variances

This is the authors' abstract. We don't add key points for this paper.

The lack of robustness of the one-way ANOVA to the heterogeneity of the within group variances is well-known (Scheffe [1959]). For two samples a robust version of the t-test has been developed (Welch [1947], Wang [1971]). For more than two samples Welch [1951] proposed a statistic based on an asymptotic confidence interval approach. An alternative robust method is to replace the denominator of the usual ANOVA F-statistic by an estimate of the variance of the numerator (Brown and Forsythe [1974]). Here we show how this latter statistic can be derived by combining individual orthonormal contrasts. This result is extended to the analysis of a two-way ANOVA and to test the lack of fit of contrasts partitioned from the mode]. A multiple comparisons test procedure is proposed which is similar to that of Scheffe [1959].