Fit a Multivariate Analysis of Variance Model
DESCRIPTION:
Returns an object of class "manova" that contains the fit for the multivariate analysis of variance of the specified model.
USAGE: 
manova(formula, data=<<see below>>, qr=F, contrasts=NULL, ...)
REQUIRED ARGUMENTS:
formula:
formula or terms describing the model. The response needs to be a matrix.
OPTIONAL ARGUMENTS:
data:
if supplied, a data frame in which the objects named in the formula are to be found. If data is omitted, the current search list is used to find the objects in formula; frequently, a data frame will have been attached.
qr:
logical flag: should the orthogonal decomposition be returned? See lm.fit.qr. If you can't imagine why you would need this, you don't.
contrasts:
a list of contrasts to be used for some or all of the factors appearing as variables in the model formula. The names of the list should be the names of the corresponding variables, and the elements should either be contrast-type matrices (matrices with as many rows as levels of the factor and with columns linearly independent of each other and of a column of one's), or else they should be functions that compute such contrast matrices.
...:
arguments to be passed to lm. In particular, the argument na.action can be a function that filters missing values from a data frame, and subset can be a vector for selecting observations (rows) from a data frame.
VALUE:
an object describing the fit. There are two cases:

if there is no Error term in the model, the object is of class "manova" which inherits from classes "maov", "mlm", "aov" and "lm". See the aov.object help file for details on the components of this object.

if there is an Error term in the model, then the object returned by aov has class "aovlist" and is a list of manova objects, one for each stratum.

DETAILS:
A manova object is essentially the same as an aov object from a multiresponse model, only the class is different. The most important difference is that there is a method for summary specific to manova objects.
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:
aov.object , aov , summary.manova .
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