THE IMPLEMENTATION OF THE ALEXANDER-GOVERN TEST IN FACTORIAL DESIGN ANALYSIS

Abstract

This study proposed to evaluate the performance of the Alexander-Govern test (AG test), Analysis of Variance (ANOVA), and t-test by analyzing the Type I error rate. The AG test is regarded as a reliable
control Type I error rate. This technique is insensitive in the presence of heteroscedasticity under a normal distribution. Simulation research was carried out using Statistical Analysis Software (SAS) to assess the effectiveness of the tests that are based on the rate of Type I error. By creating the conditions that could highlight the strengths and weaknesses of each test, three variables are being manipulated: sample size, variance heterogeneity, and type of pairings. The performance of the AG tests is convincing when it is able to control the Type I error rates better compared to ANOVA under all conditions of heterogeneous variances. Meanwhile, the ANOVA performs best only when the variances are homogenous. A real data experiment was applied to validate the result. In the battery life design experiment, the p-value using the AG test and ANOVA are computed and compared. The AG test provides valid results when it can test the main effect and the interaction effect, as well as the ANOVA. With good performance in the simulation study, the AG test can be considered a good alternative
to the ANOVA when the assumptions of the homogeneity of variances are violated in the case of factorial design.