A robust single-stage method for the one-way ANOVA with unequal sample sizes and heterogeneous variances.

Abstract

Considering the prevalence of heterogeneous variances and unequal sample sizes appeared in the educational and psychological research, the present study develops a modified single-stage one-way ANOVA by employing Hill's normalizing transformation. The proposed test statistic for the single-stage ANOVA is approximately a chi-square distribution, which makes the critical values are easy to obtain. A simulation and a numerical example for the single-stage ANOVA are also presented to demonstrate the properties of the new technique. It is found that the proposed test statistic is relatively closed to the nominal level under various simulated configurations of sample size, standard deviation ratio, and number of groups. Moreover, the proposed method outperforms other competitors with respect to the empirical power. A numerical example is also demonstrated to enhance the application of the new technique and a SAS program is available at http:\\www.css.ncku.edu.tw/Edu/luh/index.