Performance of the Alexander and Govern A statistic under heteroscedasticity imposed on normal data or induced by skew: An empirical study

Analysis of variance (ANOVA) is one of the most commonly used statistical techniques, and the most powerful when the assumptions of normality and homoscedasticity are met. When data are heteroscedastic, available options include ignoring the violation, performing ANOVA on data that have been transformed to minimize (power transformation) or at least reduce (approximate transformation) the heteroscedasticity, performing ANOVA on ranked data (Kruskal-Wallis test), or using an alternative statistic. Alexander and Govern (1994) proposed the alternative statistic A which is relatively easy to compute and assess for one-way designs. A was both robust and powerful when applied to normal but heteroscedastic data. The purpose of the present study was to compare the performance of A to that of traditional ANOVA approaches using normal but heteroscedastic data as well as data in which heteroscedasticity was induced by skew. Simulated data from normal, lognormal, and variable skew distributions were analyzed. Type I error rates (...