title: Maximum likelihood analysis for heteroscedastic one-way random effects ANOVA in interlaboratory studies.
abstract: 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.
authors.affiliation: Statistical Engineering Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-0001, USA. vangel@cam.nist.gov
authors.forename: M G
authors.initials: MG
authors.lastname: Vangel
authors.forename: A L
authors.initials: AL
authors.lastname: Rukhin
mesh_terms: D000704:Analysis of Variance; D001499:Bayes Theorem; D001699:Biometry; D016001:Confidence Intervals; D007753:Laboratories / Q000706:statistics & numerical data; D016013:Likelihood Functions