Multivariate Data Analysis Chapter6 – Multivariate Analysis of Variance

What Is Multivariate Analysis of Variance (MANOVA)? Univariate Procedures For Assessing Group Differences The t Test Analysis of Variance (ANOVA) Multivariate Analysis of Variance (MANOVA) The Two-Group Case: Hotelling's T2 The k-Group Case: MANOVA

Chapter 6 Differences Between MANOVA and Discriminant Analysis A Hypothetical Illustration of MANOVA When Should We Use MANOVA? Control of Experimentwide Error Rate Differences Among A Combination of Dependent Variables

A Decision Process for MANOVA Stage 1: Objectives of MANOVA Types of Multivariate Questions Suitable for MANOVA Multiple Univariate Questions Structured Multivariate Questions Intrinsically Multivariate Questions Selecting the Dependent Measures

A Decision Process for MANOVA (Cont.) Stage 2: Issues in the Research Design of MANOVA Sample Size Requirements---Overall and by Group Factorial Designs---Two or More Treatments Selecting Treatments A Hypothetical Example Interpreting Interaction Terms MANOVA Counterparts of Other ANOVA Designs Using Covariates---ANCOVA and MANCOVA Objectives of Covariance Analysis Selecting Covariates A Special Case of MANOVA: Repeated Measures

A Decision Process for MANOVA (Cont.) Stage 3: Assumptions of ANOVA and MANOVA Independence Equality of Variance-Covariance Matrices Normality Linearity and Multicollinearity Among the Dependent Variables Sensitivity to Outliers

A Decision Process for MANOVA (Cont.) Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit Criteria for Significance Testing Statistical Power of the Multivariate Tests Increasing Power in ANOVA and MANOVA Using Power in Both Planning and Analysis Calculating Power Levels The Effects of Dependent Variable Multicollinearity on Power

A Decision Process for MANOVA (Cont.) Stage 5: Interpretation of the MANOVA Results Evaluating Covariates Assessing the Dependent Variate Identifying Differences Between Individual Groups Post Hoc Methods A Priori or Planned Comparisons Stage 6: Validation of the Results

Example 1: Difference Between Two Independent Groups A Univariate Approach: The t Test Stage 1: Objectives of the Analysis Stage 2: Research Design of the ANOVA Stage 3: Assumptions in ANOVA Stage 4: Estimation of the ANOVA Model and Assessing Overall Fit Stage 5: Interpretation of the Results

Example 1: Difference Between Two Independent Groups (Cont.) A Multivariate Approach: Hotelling's T2 Stage 1: Objectives of the MANOVA Stage 2: Research Design of MANOVA Stage 3: Assumptions in MANOVA Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit Stage 5: Interpretation of the Results

Example 2: Difference Between k Independent Groups A Univariate Approach: k-Groups ANOVA Stage 1: Objectives of the ANOVA Stage 2: Research Design of ANOVA Stage 3: Assumptions in ANOVA Stage 4: Estimation of the ANOVA Model and Assessing Overall Fit Stage 5: Interpretation of the Results

Example 2: Difference Between k Independent Groups (Cont.) A Multivariate Approach: k-Groups MANOVA Stage 1: Objectives of the MANOVA Stage 2: Research Design of the MANOVA Stage 3: Assumptions in MANOVA Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit Stage 5: Interpretation of the Results

Example 3: A Factorial Design for MANOVA with Two Independent Variables Stage 1: Objectives of the MANOVA Stage 2: Research Design of the MANOVA Stage 3: Assumptions in MANOVA Stage 4: Estimation of the MANOVA Model and Assessing Overall Fit Stage 5: Interpretation of the Results

Your Assignment