Performance Evaluation of Different Tests for Location Parameters

In this article, our objective is to evaluate the performance of different tests which are used to compare the equality of more than two location parameters. We have considered six tests (including some commonly used) in this study, one of which is parametric and the others are nonparametric. These tests include the usual F test (Fisher and Mackenzie, 1923 Fisher , R. A. , Mackenzie , M. A. ( 1923 ). Studies in crop variation. II. The manurial response of different potato . Journal of Agricultural Science 13 : 311 – 320 .Crossref], Web of Science ®] , Google Scholar]), Kruskal–Wallis test (Kruskall and Wallis, 1952 Kruskall , W. H. , Wallis , W. A. ( 1952 ). Use of ranks in one-criterion variance analysis . Journal of American Statistical Association 47 : 583 – 621 .Taylor & Francis Online], Web of Science ®] , Google Scholar]), Kolmogorov–Smirnov test (David, 1958 David , H. T. ( 1958 ). Three-sample Kolnogorov–Smirnov test . The Annals of Mathematical Statistics 29 : 842 – 851 .Crossref] , Google Scholar]), the g test (Stekler, 1987 Stekler , H. O. ( 1987 ). Who forecasters better? Journal of Business and Economic Statistics 5 : 155 – 158 .Taylor & Francis Online], Web of Science ®] , Google Scholar]), f test (Batchelor, 1990 Batchelor , R. A. ( 1990 ). All forecasters are equal . Journal of Business and Economic Statistics 8 : 143 – 144 .Taylor & Francis Online], Web of Science ®] , Google Scholar]), and Extension of Median test (as given in Daniel, 1990 Daniel , W. W. ( 1990 ). Applied Nonparametric Statistics. , 2nd ed. Duxbury Classic Series , Boston . Google Scholar]). Performance of these tests are compared under different symmetric, skewed and contaminated probability distributions that include Normal, Cauchy, Uniform, Laplace, Lognormal, Exponential, Weibull, Gamma, t, Chi-square, Half Normal, Mixed Weibull, and Mixed Normal. Performances of these tests are measured in terms of power. We have suggested appropriate tests which may perform better under different situations. It is expected that researchers will find these results useful in decision making.