The efficiency of parametric and non-parametric statistics on location testing with multiple population groups

Abstract

          This research aimed to study the efficiency of parametric and non-parametric statistics on location testing with multiple population groups. The statistical techniques applied were one-way ANOVA (F test), the Kruskal-Wallis test (K-W test), and the Van der Waerden normal–scores test for k independent samples (V-W test). The data were simulated by Monte Carlo techniques with program R. The determined conditions were population with normal distribution, negative skewness and platykurtic distribution  ( = -0.75, K = 2.80) and positive skewness and leptokurtic distribution ( = 0.75, K = 3.60). Additionally, the sample sizes were 10 (small), 25, 50 (medium) and 100 (large). The sample were divided into 3, 4, and 5 groups with equal/non-equal variance. The hypotheses were tested at significant levels of 0.05 and 0.01. The results showed that the population was normal distribution, the tested statistics showing robustness and having highest power of the test for small sample were F test and K-W test, for medium sample was K-W test, and for large sample were F test, K-W test, and V-W test.  When the population was negative skewness and platykurtic distributions, the tested statistics showing robustness and having highest power of the test for small and medium samples was V-W test. For large sample with equal variance, the tested techniques were F test, K-W test, and V-W test. For non-equal variance, the tested technique was F test. Finally, when population was positive skewness and leptokurtic distribution, the tested statistics showing robustness and highest power of the test for small sample were K-W test and V-W test, for medium sample was V-W test, and for large sample with equal variance were F test, K-W test, and V-W test, and with non-equal variance was F test.