**Multivariate
Analysis of Variance (MANOVA)**

Multivariate
analysis of variance (MANOVA) is simply an ANOVA with several dependent
variables. ANOVA tests for the difference in means between groups, while MANOVA
tests for the difference in two or more vectors of means (e.g., changes on
total cholesterol, triglyceride and low density lipid).

For
multivariate responses, the problems to use separate univariate
tests are:

(1)
Separate univariate tests will inflate
type I error (e.g. 10 responses, separate t test at α=0.05, then at least
1 type I error ≥ (1-0.95)^{10} ≈0.40);

(2)
Univariate tests
ignore correlations among responses;

(3)
Groups may not differ on any single response, but may differ on
several responses jointly.

Multivariate
test uses overall α=0.05, and takes into account of correlations among
responses, and can detect the joint difference.

Below is the **sample
input window**

Below is the **sample
output**:

Multivariate ANOVA for:

Y0

Y1

Y2

Y3

Y4

Y5

Df
Pillai approx F num Df
den Df
Pr(>F)

factor(DOSE) 2 0.29850
5.5847 12 382 7.739e-09 ***

Residuals 195

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Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1