One—way fixed effects analysis of variance when the error varianes may be unequal

It is well known that the F—test for the one—way Analysis of Variance is sensitive to the assumption of homogeneity of error variances (see for example Scheffie, 1959, page 351, Welch, 1951,Jones, 1951 Box,1954, Brown and Forsythe, 1974, Bishop and Dudewicz, 1978, Tan and Tabatiabai, 1986). ]These references discuss the effect on the type I error and usually conclude that the effect is nor serious when the group sizes are equal. The alternatives suggested, and there are several in these references, do not seem to have been adopted generally. Just what is the effect of heterogeneity of the F—test with respect to both size and power? Is it correct to conclude that the effect is “not serious” when the groups are the same size? If there is a serious problem is there a practical alternative which is easy to use? These questions are answered here.