Testing the equality of coefficients of variation and comparisons

In this graduate dissertation, the test statistics that are used to test hypotheses, which are about the equality of the coefficients of variation, have been introduced and compared . A simulation has been prepared for the comparative study. The simulation has been designed for a different numbers of population (k=2, 3, 4, 5 and 6), a different sample sizes (n=10, 15, 20, 30, 40, 50 and 100) and a different levels of I. type error (?=0,01, 0,05 and 0,10). The purpose of the study is to compare the test statistics that are used to test the equality of coefficient of variation in terms of I. type error and the power of the test. The results of the comparisons regarding the I. type error suggest that in testing the hypothesis about the equality of two coefficient variation, the good test method when the sample size is taken a number particularly as 10 can be suggested as Square Rank Test (SRT). The Score Test of Gupta and Ma, Likelihood Ratio Test of Nairy and Rao, and the Score Test have given much worse results compared to others tests. In a relatively small sample size, Non-Central t Test (MOT) as k increases; the test results get closer to nominal values and become consistent. In all k cases, as the sample size for all tests, experimental I. type error value get closer to value. Whereas in the case of k=2, even when the sample size is 100, the value elicited from KRT and SGM tests keep being distant from value. As the k value increases, it is apparent to observe the bad results in Wald Test. In the cases where sample size is less than 30, it is not likely to observe any betterment in results of Likelihood Ratio Test of Nairy and Rao, Likelihood Ratio Test of Gupta and Ma, in all values of k. As and k values increase, WTT and MAO continue to produce good results; the betterment in the results of MT can be clearly seen. It can be observed that when the sample size increases, there is betterment in the results. In all cases of k, the tests whose results are not getting any better despite the increase in k are SGM, SNR, and KRT tests. The research conducted in terms of comparing the power of the test, SGM, SNR, and KRT have revealed the worst scores. Hence, it would be more suitable to use alternative tests instead of these ones. For instance, in the event that the k number of coefficient variables is different from each other, OGM and ONM give quite good results. When some of the k number of coefficient variables is equal to each other, in WT test the power of the test is higher. The results that can be reached is that if few of the k number of coefficient variables is different, the use of the test WT can be suggested. Even when the sample size is big enough (n=50 and 100) it has been observed that the results of KRT are worse than those of the other tests. The results elicited from the comparisons used in this research concerning the power of the test overlap with the statistical theory.