New monte carlo results on the robustness of the anova f, w and f statistics
Titel:
New monte carlo results on the robustness of the anova f, w and f statistics
Auteur:
Wilcox, Rand R. Char1in, Ventura L. Thompson, Karen L.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 15 (1986) nr. 4 pagina's 933-943
Jaar:
1986
Inhoud:
Because the usual F test for equal means is not robust to unequal variances, Brown and Forsythe (1974a) suggest replacing F with the statistics F or W which are based on the Satterthwaite and Welch adjusted degrees of freedom procedures. This paper reports practical situations where both F and W give * unsatisfactory results. In particular, both F and W may not provide adequate control over Type I errors. Moreover, for equal variances, but unequal sample sizes, W should be avoided in favor of F (or F ), but for equal sample sizes, and possibly unequal variances, W was the only satisfactory statistic. New results on power are included as well. The paper also considers the effect of using F or W only after a significant test for equal variances has been obtained, and new results on the robustness of the F test are described. It is found that even for equal sample sizes as large as 50 per treatment group, there are practical situations where the F test does not provide adequately control over the probability of a Type I error.