<b>A study about the size and power of <em>t-Student</em> and <em>Wilcoxon</em> tests</b> - DOI: 10.4025/actascitechnol.v27i1.1495

Abstract

A typical problem in statistics data analysis consists in testing a null hypothesis H0 : µ= µ0 versus an alternative H1 : µ≠ µ0 , where µ0 is some specific value of the true parameter µ. From a random sample with normal distribution with mean µ and variance σ², both unknown, we might use the well known t-student test. As an alternative to the usual t-student test, under the symmetric supposition, we can use the nonparametric Wilcoxon on test (Conover, 1971). In this paper, a Monte-Carlo simulation study was conducted to calculate the empirical size and power of the t-student and Wilcoxon tests. In this study, several instances were considered. For the size of both tests, we considered sample sizes equal to n = 10, 20, K , 90, 100 simulated from Normal, Laplace, Uniform, t-Student and Logistic distributions, under the null hypothesis with σ = 0. In the power study, from the same sample sizes and for all distributions, random samples were simulated from the alternative hypothesis considering µ0 = -1.0, -0.9, K , 0.9, 1.0