An Empirical Comparison of Power of Two Independent Population Tests under Different Underlined Distributions

Abstract

Determining whether sample differences in central tendency represent real differences in parent populations is a typical issue in applied research. If the conditions of normality, homogeneity of variance, and independence of errors are met, the t-test can be used for a two sample instance (two groups). However, the nonparametric equivalent is taken into account when these presumptions are violated. In order to determine which test is most effective and resilient to a certain distribution and sample size when samples are obtained from separate populations, the study compares the effectiveness and sensitivity of power of four test statistics. These tests were examined under normal and some skew distributions at sample size of 5, 10, 15, 20, 25, 30, 40, 45, and 50 using simulation. The most effective test for a given distribution and sample size was chosen using the power of each test computed. The study found that when data are taken from a normal distribution and tested at small and large sample sizes, respectively, the t-test and Welch test have the highest power, while the Median is the most resistant to uniform and gamma, and the Man-Whitney test is the most reliable for exponential distributions.