Abstract
This chapter discusses the monotonicity and unbiasedness properties of univariate analysis of variance (ANOVA) and multivariate analysis of variance (MANOVA) tests. The four tests discussed in the chapter are likelihood-ratio test, Roy's maximum-root test, Lawley–Hotelling's trace test, and the Bartlett–Nanda–Pitlai trace test. The conditions under which the power function of an invariant test increases monotonically are also discussed in the chapter. It also presents a minor extension of Anderson's result of the theorem of the multivariate case, the monotonicity of the power functions of UMP invariant tests in two special cases, mathematical preliminaries, study on monotonicity in the general case, general MANOVA models, and various theorem and lemmas.
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