Multivariate Data Analysis Chapter6 � Multivariate Analysis by DgjB6vi

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

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

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

   Stage    Objectives of the MANOVA
            1:
   Stage    Research Design of the MANOVA
            2:
   Stage    Assumptions in MANOVA
            3:
   Stage    Estimation of the MANOVA Model
            4:
             and Assessing Overall Fit
   Stage 5: Interpretation of the Results
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