The robustness of H statistic with hinge estimators as the location measures

In testing the equality of location measures, the classical tests such as t-test and
analysis of variance (ANOVA) are still among the most commonly chosen procedures. These procedures perform best if the assumptions of normality of data and homogeneity of variances are fulfilled. Any violation of these assumptions could jeopardize the result of such classical tests. However, in real life, these
assumptions are often violated, and therefore, robust procedures may be preferable. This study proposed two robust procedures by integrating H statistic with adaptive trimmed mean using hinge estimators, HQ and HQ₁. The proposed procedures are denoted as HTᵸᵟ and HTᵸᵟ₁ respectively. H statistic is known for its ability to control Type I error rates while ̂Tᵸᵟ and ̂Tᵸᵟ₁ are the robust location estimators.
The method of adaptive trimmed mean trims data using asymmetric trimming technique, where the tail of the distribution is trimmed based on the characteristic of that particular distribution. To investigate on the performance (robustness) of the procedures, several variables were manipulated to create conditions which are known to highlight its strengths and weaknesses. Such variables are the amount of
trimming, number of groups, balanced and unbalanced sample sizes, type of distributions, variances heterogeneity and nature of pairings. Bootstrap method was used to test the hypothesis since the distribution of H statistic is unknown. The integration between H statistic and adaptive trimmed mean produced robust procedures that are capable of addressing the problem of violations of the
assumptions. The findings showed that the proposed procedures performed best in terms of controlling the Type I error rate with different trimming amounts; the HTᵸᵟ performed best with 20% trimming, while 15% was best for the ̂HTᵸᵟ₁. In addition, both procedures were also proven to be more robust than the classical tests of parameteric (t-test and ANOVA) and non-parametric (Mann Whitney and
Kruskal-Wallis).