Abstract :
Several articles deal with the effects of inhomogeneous variances in one way analysis of variance (ANOVA). A very early investigation of this topic was done by Box (1954). He supposed, that in balanced designs with moderate heterogeneity of variances deviations of the empirical type I error rate (on experiments based realized ) to the nominal one (predefined for H0) are small. Similar conclusions are drawn by Wellek (2003). For not so moderate heterogeneity (e.g. 1 :2 :3:1:) Moder (2007) showed, that empirical type I error rate is far beyond the nominal one, even with balanced designs. In unbalanced designs the difficulties get bigger. Several attempts were made to get over this problem. One proposal is to use a more stringent level (e.g. 2.5% instead of 5%) (Keppel & Wickens, 2004). Another recommended remedy is to transform the original scores by square root, log, and other variance reducing functions (Keppel & Wickens, 2004, Heiberger & Holland, 2004). Some authors suggest the use of rank based alternatives to Ftest in analysis of variance (Vargha & Delaney, 1998). Only a few articles deal with two or multifactorial designs. There is some evidence, that in a two or multi-factorial design type I error rate is approximately met if the number of factor levels tends to infinity for a certain factor while the number of levels is fixed for the other factors (Akritas & S., 2000, Bathke, 2004). The goal of this article is to find an appropriate location test in an oneway analysis of variance situation with inhomogeneous variances for balanced and unbalanced designs based on a simulation study.
