The test for the homogeneity of several populations is a common issue in many application fields. The well-known results related to this issue include the analysis of variance (ANOVA) for normal populations and the Kruskal Wallis Test (KWT) for nonparametric populations, but there is no general result on the test for the homogeneity of parametric populations. In this paper, the likelihood ratio test (LRT) statistic is constructed to test for the homogeneity of several populations which are the members of a parametric family. It is shown that under some regularity conditions and the null hypothesis all distribution functions of the populations are the same, and the limiting distribution of the LRT statistic  is chi-squared distribution. This result fills in a gap between ANOVA for normal populations and KWT for nonparametric populations.