Comparison of Two Sample Tests Using Both Relative Efficiency and Power of Test

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 erroneous 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 especially, independent samples. The paper examines the efficiency and sensitivity of four test statistics 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 distribution, 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.