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About 10,000 papers for “Multivariate analysis of variance”

Multivariate Analysis of Variance,

Gilley,John G. · Defense Technical Information Center (DTIC) · 1971

Multivariate procedures are explained in the report in terms of corresponding univariate procedures. Multivariate extensions of the analysis of variance are given. A computer program listing of a two-way multivariate analysis of variance and an actual surveillance problem is included. A comparison was made between the results of the analysis as it was run using separate analysis of variance tests and the results of th multivariate analysis of variance. The material presented in this report is largely based on a class in Multivariate Analysis given at the Unitersity of Tennessee by Dr. Clyde Y. Kramer of Virginia Polytechnic Institute. (Author)

Cited by 0

Multivariate Analysis of Variance

Alvin C. Rencher · Wiley series in probability and statistics · 2002

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.

Cited by 8

Multivariate Analysis of Variance.

D. D. V. Morgan, James H. Bray, Scott E. Maxwell · Journal of the Royal Statistical Society Series D (The Statistician) · 1987

Introduction to Multivariate Analysis of Variance Omnibus MANOVA Tests Analyzing and Interpreting Significant MANOVAs Causal Models Underlying MANOVA Analyses Complex Designs Overview of Computer Programs for MANOVA

Cited by 456

Multivariate Analysis of Variance

Donald F. Morrison · Encyclopedia of Biostatistics · 2005

Abstract The multivariate analysis of variance (MANOVA) is an extension of the univariate analysis of variance to multidimensional, or vector‐valued, observations. The same experimental design or treatment layout applies to each of the observed response variables. The univariate assumption of a normal distribution is replaced by the multivariate normal distribution for the data vectors and the random error components in the mathematical model of the design.

Cited by 28