Multivariate Analysis Of Variance

1 Multivariate Analysis of Variance (MANOVA) • • •

MANOVA has the same means for all the dependent variables ANOVA has individual means Can perform a stepdown F analysis for assumed highly correlated dependent variables if Bartlett’s test of sphericity is significant at alpha level of 0.05, if not correlated use ANOVA instead

When to use MANOVA • • • • • •

Cell sizes should be large of > 30 subjects Not necessary to have equal cell sizes but small cell size / largest cell size should be < 1/ 1.5 is preferred Tests for uni- and multi-variate normality – should follow in order to run There must be linear relationships (linearity) among all pairs of dependent variables to be assumed Must have assumption of homogeneity of variance/covariance matrices using Box’s M test and must be non-significant (p > 0.001 level is recommended as the test is very sensitive) When correlation among dependent variables are high, multicollinearity and Singularity exist when determinant of within-cell correlation matrix is near 0 ( < 0.0001) of Log (Determinat) is < - 9.21034.

How to use MANOVA (Example) • • • • •

To determine the influence of history on variables related to community attachment on 388 residents by filling the dependent variables scales. Alternate Hypothesis (H1): Individuals living in community prior to 1850 would have significantly larger networks, higher levels of social support and sense of community than those settled after 1850. Independent vars: (History) period of settlement from 1 = 1800-1850 and 2 = 1851-1900 Dependent vars: sense of community (soc), quality of social support (ss), network size. Conceptually and theoretically the dep vars were assumed to be related thus we can use MANOVA (see Fig 1)

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To Run MANOVA • • •

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Select Statistics menu then ANOVA Models then Multivariate to open the dialogue box. Select the dependent variables (network, soc, ss ) and > move to Dep Var box Select ind var (history) and move to Factor box then click on Define Range, for Minimum box type 1 and max type 2, then continue. (see Fig 2)

Click on Model to open the Multivariate ANOVA: Model subdialogue box. (see Fig 3)

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Select Full factorial, then in the Model options select Within cells in the Error term. In the Display box, select Multivariate tests, Univariate tests then click continue. (you can also conduct the stepdown F) Click on Options to open the Multivariate ANOVA:Options subdialogue box (see Fig 4)

In the Factor(s) select history and move to Display Means for Select Correlation, and Homogeneity tests and click Continue then OK.