Modification of ANOVA with Various Types of Means

Abstract

In calculating mean equality for two or more groups, Analysis of Variance (ANOVA) is a popular method. Following the normality assumption, ANOVA is a robust test. A modification to ANOVA is proposed to test the equality of population means. The suggested research statistics are straightforward and are compatible with the generic ANOVA statistics whereby the classical mean is supplemented by other robust means such as geometric mean, harmonic mean, trimean and also trimmed mean. The performance of the modified ANOVAs is then compared in terms of the Type I error in the simulation study. The modified ANOVAs are then applied on real data. The performance of the modified ANOVAs is then compared with the classical ANOVA test in terms of Type I error rate. This innovation enhances the ability of modified ANOVAs to provide good control of Type I error rates. In general, the results were in favor of the modified ANOVAs especially ANOVAT and ANOVATM.