Single-stage analysis of variance under heteroscedasticity

The procedures of testing the equality of normal means in the conventional analysis of variance (ANOVA) are heavily based on the assumption of the equality of the error variances. Studies have shown that the distribution of the F-test depends heavily on the unknown variances and is not robust under the violation of equal error variances. When the variances are unknown and unequal, Bishop and Dudewicz (1978) developed a design-oriented two-stage procedure for ANOVA, which requires additional samples at the second stage. In this paper we use a single-stage sampling procedure to test the null hypotheses in ANOVA models under heteroscedasticity. The single-stage procedure for ANOVA has an exact distribution and it is a data-analysis-oriented procedure. It does not require additional samples, and can reach a conclusion much earlier, save time and money. Simulation results indicate that the power of the single-stage procedure is better than the two-stage method when the initial sample size is smaller than 6, and performs well when n o is 6 or larger. Table of critical values and a numerical example are given.