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This article presents results for the maximum likelihood analysis of several groups of measurements made on the same quantity. Following Cochran (1937, Journal of the Royal Statistical Society 4(Supple), 102-118; 1954, Biometrics 10, 101-129; 1980, in Proceedings of the 25th Conference on the Design of Experiments in Army Research, Development and Testing, 21-33) and others, this problem is formulated as a one-way unbalanced random-effects ANOVA with unequal within-group variances. A reparametrization of the likelihood leads to simplified computations, easier identification and interpretation of multimodality of the likelihood, and (through a non-informative-prior Bayesian approach) approximate confidence regions for the mean and between-group variance.
Vangel et al. (Mon,) studied this question.