MANOVA
<testoptions> <detailoptions> ;
If the MODEL statement includes more than one dependent variable, you can perform multivariate analysis of variance with the MANOVA statement. The testoptions define which effects to test, while the detailoptions specify how to execute the tests and what results to display.
When a MANOVA statement appears before the first RUN statement, PROC ANOVA enters a multivariate mode with respect to the handling of missing values; in addition to observations with missing independent variables, observations with any missing dependent variables are excluded from the analysis. If you want to use this mode of handling missing values but do not need any multivariate analyses, specify the MANOVA option in the PROC ANOVA statement.
Table 25.3 summarizes the options available in the MANOVA statement.
Table 25.3: MANOVA Statement Options
Option 
Description 

Test Options 

Specifies hypothesis effects 

Specifies the error effect 

Specifies a transformation matrix for the dependent variables 

Provides names for the transformed variables 

Alternatively identifies the transformed variables 

Detail Options 

Displays a canonical analysis of the and matrices 

Specifies the method of evaluating the multivariate test statistics 

Orthogonalizes the rows of the transformation matrix 

Displays the error SSCP matrix 

Displays the hypothesis SSCP matrix 

Produces analysisofvariance tables for each dependent variable 
You can specify the following options in the MANOVA statement as testoptions in order to define which multivariate tests to perform.
You can specify the following options in the MANOVA statement after a slash as detailoptions:
The following statements give several examples of using a MANOVA statement.
proc anova; class A B; model Y1Y5=A B(A); manova h=A e=B(A) / printh printe; manova h=B(A) / printe; manova h=A e=B(A) m=Y1Y2,Y2Y3,Y3Y4,Y4Y5 prefix=diff; manova h=A e=B(A) m=(1 1 0 0 0, 0 1 1 0 0, 0 0 1 1 0, 0 0 0 1 1) prefix=diff; run;
The first MANOVA statement specifies A
as the hypothesis effect and B
(A
) as the error effect. As a result of the PRINTH option, the procedure displays the hypothesis SSCP matrix associated with the A
effect; and, as a result of the PRINTE option, the procedure displays the error SSCP matrix associated with the B
(A
) effect.
The second MANOVA statement specifies B
(A
) as the hypothesis effect. Since no error effect is specified, PROC ANOVA uses the error SSCP matrix from the analysis as
the matrix. The PRINTE option displays this matrix. Since the matrix is the error SSCP matrix from the analysis, the partial correlation matrix computed from this matrix is also produced.
The third MANOVA statement requests the same analysis as the first MANOVA statement, but the analysis is carried out for variables transformed to be successive differences between the original dependent variables. The PREFIX=DIFF specification labels the transformed variables as DIFF1, DIFF2, DIFF3, and DIFF4.
Finally, the fourth MANOVA statement has the identical effect as the third, but it uses an alternative form of the M= specification. Instead of specifying a set of equations, the fourth MANOVA statement specifies rows of a matrix of coefficients for the five dependent variables.
As a second example of the use of the M= specification, consider the following:
proc anova; class group; model dose1dose4=group / nouni; manova h = group m = 3*dose1  dose2 + dose3 + 3*dose4, dose1  dose2  dose3 + dose4, dose1 + 3*dose2  3*dose3 + dose4 mnames = Linear Quadratic Cubic / printe; run;
The M= specification gives a transformation of the dependent variables dose1
through dose4
into orthogonal polynomial components, and the MNAMES= option labels the transformed variables as LINEAR, QUADRATIC, and
CUBIC, respectively. Since the PRINTE option is specified and the default residual matrix is used as an error term, the partial
correlation matrix of the orthogonal polynomial components is also produced.
For further information, see the section Multivariate Analysis of Variance in Chapter 42: The GLM Procedure.