MANOVA MANOVA MANCOVA Profile Analysis 2004 10 29

MANOVA 多變量變異數分析 MANOVA MANCOVA Profile Analysis 2004. 10. 29 1

MANOVA的統計原理 ANOVA MANOVA SS用SSCP（cross-product）代替 SSCC為依變項觀察值就多重依變項所形成的矩陣概念來計算得出 SSCPtotal=SSCPbetween+SSCPwithin 5

Assessing DVs (Roy-bargmann stepdown) • When the main effect is significant in MNOVA, the researcher has • • • planned to discover which DVs are affected. If correlations among DVs are zero, univariate ANOVA give the relevant information about their importance. Preventing from inflated Type one error due to multiple testing, more stringent alpha are required. The problem of correlated DVs is resolved by Roy-Bargmann Stepdown Analysis. – – – 1) Decide the priorities of each DV. 2) the highest-priority DV → univariate ANOVA 3) the rest of the DVs → ANCOVA Each of successive DV is tested with higher-priority DVs as covariate to test. 4) if significant → add to the combination of DVs already tested 11

多變量檢定指標 • Pillai’s Trace • Wilds’ Lambda • Hotelling’s Trace • Roy’s Largest Root 12

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MANOVA For Main Effect I 17

MANOVA For Main Effect II 18

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SSCP的計算 25

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General Purpose and Description • Profile analysis (Repeated measures MANOVA) is a • special application of MANOVA to a situation where there are several DVs, all measured on the same scale. The set of DVs can either come from one DV measured several different times, or several different DVs all measured at one time. • There is also another extension of the analysis where several different DVs are measured at several different times, called the doubly-multivariate design. 41

The difference between repeated measures MANOVA and ANOVA • Repeated measures MANOVA used multivariate approach is an alternative to repeated measures ANOVA. Univariate repeated measures ANOVA multivariate repeated measures MANOVA Profile Analysis 42

Parallelism and Flatness of Profile Analysis • The two major tests of profile analysis are parallelism and flatness. • To univariate repeated measures ANOVA, the parallelism test is the test of interaction, and the flatness is the test of main effect. 43