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• W4206519694 abstract "In this chapter, univariate analysis of variance is extended to multivariate analysis of variance (MANOVA), in which several variables are measured on each experimental unit. For each case, the univariate analysis of variance is reviewed before extending to the corresponding multivariate analysis of variance. The basic multivariate models covered include the one-way model, the two-way model, higher order fixed effects models, mixed models, repeated measures designs, and growth curves. There are four commonly used test statistics in most MANOVA software: Wilks' Λ, Roy's θ, Pillai's V(s), and the Lawley–Hotelling statistic U(s). Wilks' Λ has many useful properties and is the most popular. Since exact p-values are not given in the program packages, tables for all four test statistics are provided in Appendix A so that an exact text can be made. The four test statistics have different power for different configurations of the population mean vectors. Measures of fit similar to R2 from multiple regression are given for the MANOVA model. Methods are given for checking on the assumptions of MANOVA for any given data set. Contrasts in means in the univariate case are extended to contrasts in mean vectors in the multivariate case. Various tests on individual variables are discussed for use following rejection of the multivariate hypothesis by any of the four tests. The two-sample profile analysis of Chapter 5 is extended to several (k) groups. The hypotheses are that the k profiles are (1) parallel, (2) all at the same level, and (3) flat. Repeated measures designs are covered up to a complexity level of two within-subjects factors and two between-subjects factors. Univariate and multivariate approaches to repeated measures are discussed, with the emphasis on the multivariate approach. Growth curves result when human or animal subjects respond to a treatment of stimulus at successive time periods. Polynomial curves are fit to the responses, and curves for different samples are compared. A subvector of variables can be tested for its contribution to Wilks' Λ. A subset of variables can be selected in a stepwise fashion. Numerical illustrations using real data are provided for most techniques covered in this chapter. The large problem set at the end of the chapter provides derivations of certain techniques in the chapter and further illustrates most techniques with real data." @default.
• W4206519694 created "2022-01-25" @default.
• W4206519694 date "2002-02-22" @default.
• W4206519694 modified "2023-10-17" @default.
• W4206519694 title "Multivariate Analysis of Variance" @default.
• W4206519694 doi "https://doi.org/10.1002/0471271357.ch6" @default.
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