explain the difference between univariate and multivariate ANOVA
discuss the advantages of a multivariate approach to a univariate approach in testing a hypothesis
State the assumptions for the use of MANOVA
Discuss the types of statistical techniques used for MANOVA
Interpret SPSS outputs from using MANOVA.
What is the Multivariate Analysis of Variance (MANOVA)?
The theoretical construct of Mulitivariate Analysis of Variance of MANOVA was introduced by S.S. Wilks. However, it was only recently that appropriate statistical tools were developed and with computers, MANOVA has become an important tool for educational researcher interested in analysing data.
MANOVA is an extension of ANOVA which is a univariate procedure. We use ANOVA to test for differences between groups. ANOVA is termed a univariate procedure because we use it to test for differences between groups based on only ONE dependent variable.
High Income 20.34 2.1
Middle Income 19.01 2.2
Low Income 18.23 1.9
Mean Std. Deviation
Middle Income 19.01 2.2 30.1 1.9
High Income 20.34 2.1 34.2 2.1
Low Income 18.23 1.9 28.7 2.0
Mean Std. Deviation Mean Std. Deviation
Self-Esteem Parental Bonding
(ANOVA) Univariate Analysis
- only ONE dependent variable. i.e. Self-Esteem
Self-Esteem
(MANOVA) Multivariate Analysis
- TWO dependent variable. i.e. Self-Esteem & Parental Bonding
See the example below. Here, you are interested in establishing whether there is a difference in self-esteem between students from high income, middle income and low income households. The dependent variable is 'self-esteem' which may be measured using a 4-point Likert scale.
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What is the Multivariate Analysis of Variance (MANOVA)?
The theoretical construct of Mulitivariate Analysis of Variance of MANOVA was introduced by S.S. Wilks. However, it was only recently that appropriate statistical tools were developed and with computers, MANOVA has become an important tool for educational researcher interested in analysing data.
MANOVA is an extension of ANOVA which is a univariate procedure. We use ANOVA to test for differences between groups. ANOVA is termed a univariate procedure because we use it to test for differences between groups based on only ONE dependent variable. MANOVA is also used for testing differences but is called a multivariate procedure because we use it to test differences between groups across MORE THAN ONE dependent variable simultaneously.