# 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