An evaluation of some non‐parametric and parametric tests for location equality

The Kruskal‐Wallis and normal scores non‐parametric tests of location equality are compared to the parametric analysis of variance F test. In addition to quantifying and manipulating degrees of variance heterogeneity due to combining heterogeneous variances with unequal sample sizes, the tests are compared for their sensitivity, as well as rates of Type I error, under varying conditions of mean variability when sampling from Gaussian and exponential distributions. Even though the asymptotic literature (Pratt, 1964; Puri, 1964) favours the normal scores test, it is found that the Kruskal‐Wallis test is preferable to the normal scores test while the choice between the Kruskal‐Wallis and analysis of variance tests depends upon population shape.