GEOG 4/517:  Geographic Data Analysis
MANOVA and Discriminant Analysis

Multivariate Analysis of Variance (MANOVA)

Multivariate analysis of variance, or MANOVA, like univariate analysis of variance is aimed at testing the null hypothesis that the means of groups of observations are identical.  Rejection of this hypothesis is generally accompanied by the scientific conclusion that the groups of observations are indeed different, or were generated by some different process, or come from different underlying populations.

Illustration

• The univariate analysis of variance situation aov.gif
• The multivariate analysis of variance situation manova.gif

Details of MANOVA

Examples of MANOVA

Discriminant Analysis

Discriminant analysis has several interrelated objectives that include:

• identification of how one or more groups of observations differ as described by one or more, usually several, interrelated variables
• identification of which variables best distinguish among the different groups
• assignment or classification of new observations to one or another of the groups based on the values of the variables

In short, the analysis can be thought of as answering the related questions:  Are the groups of observations different, and if so, how are they different?

Illustration

• The discriminant analysis situation:  discrim1.gif

Details of discriminant analysis

Examples of discriminant analysis

Readings: 

Manley (Multivariate Statistical Methods...) Ch. 5