Comparing the power of several tests about specific populations

Abstract

The t-test, Mann-Whitney test and median test are three tests that can be used to test for the difference in location parameters. We compared powers of the three tests under a variety of population distributions (Cauchy distribution, exponential distribution, log-normal distribution, mixed normal distribution, normal distribution, uniform distribution) through a simulation study. Each test was performed 10,000 times under the same conditions. In every case, equal sizes of 10, 15, 20 and 25 were used. The powers of the tests were estimated, based on the number of times the null hypothesis was rejected as divided by 10,000. The results of the simulation study indicated that the t-test was powerful when the underlying distributions were normal, uniform and exponential about sample size of 10. The Mann-Whitney test was powerful when the underlying distributions was mixed normal about 75% N(0,1) and 25% N(3,36), 80% N(0,1) and 20% N(2,25), log-normal, exponential about sample size of 15, 20 and 25. Also, the median test had the largest powers when the Cauchy distribution.