ON THE COMPARISON OF THE WELCH TEST AND THE SINGLE-STAGE TEST: A SIMULATION STUDY

Abstract. It is known that using the F test for testing the equality of means in a one-way ANOVA is misleading when the assumption of equal population variances is violated. When the variances are unknown and unequal, Welch [1] developed the so-called Welch test and Chen and Chen [2] developed the single-stage test for ANOVA. In this paper, Welch and single-stage tests are compared in terms of their powers and the reject ratios of the hypothesis when the hypothesis is true. Simulation results indicate that the power of the single-stage test is better than the Welch test and that this test performs well in terms of the reject ratios for small number of populations and sample sizes. 1