## Project

**Investigation of Location-Scale Nonparametric Tests and Their Implementation in**

**SAS For Two-sample Problem**

Freeh N. Alenezi

Department of Mathematics, Zulfi College of Science, Majmaah University

Department of Statistics, West Virginia University.

**Abstract**

Parametric statistical methods require assumptions, one of which is the normality assumption that is often difficult to meet. In contrast, nonparametric statistical methods do not require a normal distribution in a given population. This report focuses on the implementation of location-scale nonparametric tests in SAS for two-sample problem. The location-scale nonparametric tests, Lepage and Cucconi tests, the location test despite any possible difference in variability between two groups, Permutation Test with Brunner & Munzel statistic, and the location nonparametric test, Wilcoxon Rank Sum test, were applied on different random samples to assist their performance. The Permutation Test with Brunner & Munzel statistic was observed to have the best performance among other tests in Part 1. In Part 2, the P-values for all location-scale nonparametric tests have no significant difference with respect to small and large means and variances for the generated random samples. The P-values of the Wilcoxon Rank Sum test have no significant difference from the P-values of the Permutation Test with Brunner & Munzel statistic where the latter has significantly the smallest P-values among other tests.