Key points are not available for this paper at this time.
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.
Brown et al. (Sun,) studied this question.