Open Journal of Statistics, 2016, 6, 331-345 Published Online April 2016 in SciRes. http://www.scirp.org/journal/ojs http://dx.doi.org/10.4236/ojs.2016.62029 How to cite this paper: Umeh, E.U. and Eriobu, N.O. (2016) Comparison of Two Sample Tests Using Both Relative Efficiency and Power of Test. Open Journal of Statistics, 6, 331-345. http://dx.doi.org/10.4236/ojs.2016.62029 Comparison of Two Sample Tests Using Both Relative Efficiency and Power of Test Edith Uzoma Umeh, Nkiru Obioma Eriobu Department of Statistics, Nnamdi Azikiwe University, Awka, Nigeria Received 1 February 2016; accepted 24 April 2016; published 27 April 2016 Copyright © 2016 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract This paper, comparison of two sample tests, is motivated by the fact that in the test of significant difference between two independent samples, numerous methods can be adopted; each may lead to significant different results; this implies that wrong choice of test statistic could lead to erro- neous conclusion. To prevent misleading information, there is a need for proper investigation of some selected methods for test of significant difference between variables/subjects most espe- cially, independent samples. The paper examines the efficiency and sensitivity of four test statis- tics to ascertain which test performs better. Based on the results, the relative efficiency favours median test as being more efficient than modified median test for both symmetric and asymmetric distributions. In terms of power of test, median test is more sensitive than Modified Median (MMED) test since it has higher power irrespective of the sample sizes for both symmetric and asymmetric distribution. In terms of relative efficiency for asymmetric distribution Modified Mann- Whitney U test is more efficient than Mann-Whitney U test (MMWU), and then for symmetric dis- tribution, Mann-Whitney U test (MMWU) is more efficient than Modified Mann-Whitney in sample size of 5; but for other sample sizes considered Modified Mann-Whitney U test (MMWU) is better than Mann-Whitney. Using power of test for both symmetric and asymmetric distributions, Mann- Whitney is more sensitive than Modified Mann-Whitney U test (MMWU) because it has higher power. Keywords Asymmetric, Symmetric, Nonparametric Test, Two Sample Tests, Power of Test, Relative Efficiency 1. Introduction One of the challenges faced by researchers most especially, statisticians, is to take decisions in the presence of uncertainties. Most often, intelligent guess is made and statistical methods are applied to validate or reject any