Comparing the Power of Several Tests about Specific Populations

The t-test, Mann-Whitney test and median test are three tests that can be employed to test for the difference in location parameters. We compared powers of the three tests under a variety of population distributions (contaminated normal distribution, mixed normal 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 Mann-Whitney test was powerful when the underlying distributions were mixed normal distribution and contaminated normal distribution about sample size of 10, 15, 20 and 25. In this case, mixed normal distributions considered were 75% N(0,1) and 25% N(3,36) Also, contaminated normal distributions considered were 20% N(0,1) and 80% N(0,2).