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