Multivariate Data Analysis Chapter6

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Multivariate Data AnalysisChapter6
Multivariate Analysis of Variance
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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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