Simultaneously Testing the Equality of Means and the Equality of Variances of Several Populations

The usual practice for testing homogeneity of several populations in terms of means and variances is first to test for the equality of variances and once this assumption is found to be tenable then to test the equality of means. Singh(1986) proposes a very interesting likelihood ratio based procedure for testing homogeneity of several normal(µ,σ2) populations. Singh uses a method of combining two or more independent tests by Fisher (1950). In this paper we extend Fisher’s method based on score test statistics for several normal populations. Independence of the two score test statistics is shown. We then develop analogous procedures based on likelihood ratio test statistics and score test statistics for testing homogeneity of several negative binomial populations. In this case asymptotic independence is established for the two likelihood ratio statistics and also for the two score test statistics. Simulations are performed to study small sample properties in terms of size and power of the tests. In the simulation study we also include the ordinary likelihood ratio statistic and the ordinary score test statistic for simulataneously testing equality of means and equality of variances of several normal populations as well as for several negative binomial populations. A discussion is given and two examples are analysed