Multivariate analysis of variance (MANOVA): a practical guide to its use in scientific decision-making
Historical origins of MANOVA; Era of multivariate techniques; Sequential trends in application of multivariate techniques; Conceptual theory underlying MANOVA; Parallels between univariate ANOVA and multivariate MANOVA; Factor analysis and MANOVA; MANOVA tests of statistical significance; Differential sensitivity of test criteria related to distribution of trace; Assumptions underlying ANOVA and MANOVA; Decision strategies; Decision errors; ANOVA power analysis; MANOVA power analysis; Bonferroni t; Classic MANOVA procedure; Hummel-sligo procedure; Mixed strategy; Classic research designs; Two preliminary issues; Control checklist; Origin of all classic ANOVA designs; Extension of t test for independent groups; Extension of the t test for matched pairs (subject as his or her own control); Mixed designs; Applications of MANOVA to classic research designs; Preliminary considerations; Classic designs; Application of MANOVA to univariate designs that involve repeated measures; Distinction between MANOVA applied to univariate and multivariate repeated-measures designs; Univariate analysis of repeated measures; A univariate procedure for analyzing repeated-measures designs; Multivariate analysis of variance of repeated-measures designs; Checklist for the investigator conducting MANOVA research; Decision to conduct a study or experiment; Selection of dependent variables; Selection of a MANOVA test criterion; Statement of problem; Research design; Computer program test; Selection of MANOVA strategy; Hierarchy of hypotheses; Reporting multivariate outcomes; Hand-calculated example of one-way (simple randomized) MANOVA.
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Historical Origins of MANOVA
Conceptual Theory Underlying MANOVA
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05 level analysis of variance ANOVA and MANOVA ANOVA design appropriate Barker canonical correlation correlation covariance critical difference degrees of freedom deindividuated dent variables dimension dispersion matrices eigenvalues error sources error term F ratio F test factor analysis factor scores ﬁndings ﬁrst root ﬁrst synthetic variable freedom associated greatest characteristic root group centroids homogeneity of dispersion hypotheses independent individual inﬂuence interac intercorrelations investigator involves Lawley—Hotelling trace Lindquist Type live model main effects MANOVA test criteria matched pairs mathematics multiple comparisons number of dependent number of subjects orthogonal Pillai’s trace procedure random repeated measures repeated-measures designs required for signiﬁcance research designs Roy’s greatest characteristic Scheffé separate dependent variables shock duration shock intensity SSCP statistical power statistical signiﬁcance strategy synthetic scores Table teaching methods tests of statistical treatment effects treatment groups two-way factorial Type G Type I error univariate variance-covariance matrix weights Wilks’s lambda within-subjects