Tests of Coefficients of Variation of Normal Population

Coefficient of variation (CV) is an important and a widely used measure of dispersion. It is free from the unit of measurement and thus can be useful to compare the variability between groups of observations. A few tests were available in the past to compare the CVs of k normal populations (Gupta, C. R., Ma, S. (1996 Gupta, C. R. and Ma, S. 1996. Testing the equality of coefficients of variation in K normal populations. Common. Statist. Theory Meth, 25: 115–132. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). Testing the equality of coefficients of variation in K normal populations. Common. Statist. Theory Meth. 25:115–132). These tests are based on the sample CV and in this article three new tests are proposed based on the inverse sample coefficient of variation. The asymptotic null distribution of all the test statistics are chi-square with (k − 1) degrees of freedom (d.f.), where k refers to the number of groups. A simulation study is carried out to check the small sample adequacy of the chi-square approximation. Two of the existing tests and one of the three new tests proposed have estimated type I error rates which are very close to the nominal level. Power comparison of the tests are also carried out and the simulation results indicate that these three tests have almost the same power and it is difficult to rank any one of them as the best tests.