The robustness of the modified H-statistic in the test of comparing independent groups

• Main Authors: Abdullah, Suhaida, Teh, Kian Wooi, Syed Yahaya, Sharipah Soaad, Md Yusof, Zahayu
• Format: Article
• Language: English
• Published: Academy of Sciences Malaysia 2020
• Subjects: QA75 Electronic computers. Computer science
• Online Access: http://repo.uum.edu.my/27545/1/ASM%20Sc.%20J.%2C%2013%2C%202020%201%205.pdf; http://repo.uum.edu.my/27545/; http://doi.org/10.32802/asmscj.2020.sm26(1.27)

The H-statistic is a robust test statistic in comparing the equality of two and more than two independent groups. This statistic is one of a good alternative to the F-statistic in the analysis of variance (ANOVA). The F-statistic is good only when the distribution of data is normal with homogeneous variances. If there is a violation of at least one of these assumptions, it affects the Type I error rate of the test. The main weakness of the F-statistic is its calculation based on the mean. The mean is well-known as a very sensitive central tendency measure with 0 breakdown point, whereas the H-statistic provides a test with fewer assumptions yet powerful. This statistic is readily adaptable to any measure of central tendency, and it appears to give reasonably good results. Hence, this paper provides a detailed study on the robustness of the H-statistic and its performance using different robust central tendency measures such that the modified one-step M (MOM) estimator and Winsorized MOM estimator. Based on the simulation study, this paper also investigates the performance of the H-statistic under various data conditions. The findings reveal that this statistic performs as well as the F-statistic under normal and homogeneous variance, yet it provides better control of Type I error rate under non-normal data or heterogeneous variances or both.