On Consistency and Limitation of Independent t-test Kolmogorov Smirnov Test and Mann Whitney U test

Abstract

It is worth repeating that if data are approximately normally distributed then parametric tests (as in the modules on hypothesis testing) are more appropriate. However, there are situations in which assumptions for a parametric test are violated and a nonparametric test is more appropriate. This study was aimed to investigates the strength and Limitation of independent t-test, Mann Whitney U test and Kolmogorov Smirnov test procedures on independent samples from unrelated population, under situations where the basic assumptions of parametric are not met for different sample size. Testing hypothesis on equality of means require assumptions to be made about the format of the data to be employed. Sometimes the test may depend on the assumption that a sample comes from a distribution in a particular family; if there is a doubt, then a nonparametric tests like Mann Whitney U test or Kolmogorov Smirnov test is employed. Random samples were simulated from Normal, Uniform, Exponential, Beta and Gamma distributions. The three tests procedures were applied on the simulated data sets at various sample sizes (small and moderate) and their Type I error and power of the test were studied in both situations under study.