Create a Manova Table
DESCRIPTION:
Produces an object containing information for a manova table using one of four tests, or gives a univariate anova table for each response.
USAGE: 
summary.manova(object, univariate=F, test="pillai", alias=F,
               intercept=F)
REQUIRED ARGUMENTS:
object:
an object of class "manova" or "maov".
OPTIONAL ARGUMENTS:
univariate:
logical flag: if TRUE, then a univariate anova table is produced for each response. If FALSE, then a manova table is produced.
test:
character string partially matching one of: "pillai", "wilks lambda", "hotelling-lawley", or "roy largest" (a partial match is sufficient). This is ignored if univariate is TRUE.
intercept:
logical flag: if TRUE, then the intercept term is included in the table.
VALUE:
an object of class "summary.manova", which is a list containing components:
row.names:
a vector of character strings giving the names of the terms.
Df:
vector of the degrees of freedom for each term.
SS:
list of matrices, which are the sums of squares and crossproducts for each term.
Eigen.values:
list of the eigen values of each sums of squares and crossproducts matrix times the inverse of the matrix of sums of squares and crossproducts for the residuals.
Stats:
array of the four test statistics and corresponding test approximations for each term. The first dimension corresponds to terms, the second to the four tests. The third dimension is of length 5: the statistics, the approximate F value, the numerator degrees of freedom for the F, the denominator degrees of freedom, and the p-value from the F test.
test:
the input test.
DETAILS:
This is the method for objects of class "manova" of the generic function summary. It can be called directly on objects of class "manova" or "maov".

There is a choice of four tests, Pillai-Bartlett trace, Wilks' lambda, Hotelling-Lawley trace, and Roy's largest eigenvalue. These tests are transformed to an approximate F statistic (which is exact under some circumstances). The p-value for Roy's largest eigenvalue test is a lower bound for the true p-value. These tests are made under the assumptions of independent Gaussian errors with common variance matrices. The default test is the Pillai-Bartlett trace since it appears to be slightly more robust to failure of these assumptions than the other tests, and it is the most powerful under some reasonable conditions (see Hand and Taylor (1987) page 76).

REFERENCES:
Hand, D. J. and Taylor, C. C. (1987). Multivariate Analysis of Variance and Repeated Measures. Chapman and Hall, London.

Mardia, K. V., Kent, J. T. and Bibby, J. M. (1979). Multivariate Analysis. Academic Press, London.

Seber, G. A. F., (1984). Multivariate Observations. Wiley, New York.

SEE ALSO:
manova , summary , summary.aov , summary.mlm .
EXAMPLES: 
wafer.manova <- manova(cbind(pre.mean, post.mean) ~ maskdim +
   visc.tem + spinsp, wafer)


summary(wafer.manova) # manova table with Pillai's trace


summary(wafer.manova, univar=T) # univariate anova tables


summary(wafer.manova, test="wilk") # manova table with Wilks' Lambda