1. Multivariate Data Analysis Chapter6 – Multivariate Analysis of Variance

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. Your Assignment