Robustness of Parametric and Nonparametric Tests under Non-Normality for Two Independent Sample

Robust statistical methods have been developed for many common problems, such as estimating location, scale and regression parameters. One motivation is to provide methods with good performance when there are small departures from parametric distributions. This study was aimed to investigates the performance oft-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 non-parametric tests like Mann Whitney U test orKolmogorov 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. Keywords - Non-normal,Independent Sample, T-test,Mann Whitney U test and Kolmogorov Smirnov test.