summary.manova
Summary Method for Multivariate Analysis of Variance
A summary
method for class "manova"
.
 Keywords
 models
Usage
"summary"(object, test = c("Pillai", "Wilks", "HotellingLawley", "Roy"), intercept = FALSE, tol = 1e7, ...)
Arguments
 object
 An object of class
"manova"
or anaov
object with multiple responses.  test
 The name of the test statistic to be used. Partial matching is used so the name can be abbreviated.
 intercept
 logical. If
TRUE
, the intercept term is included in the table.  tol
 tolerance to be used in deciding if the residuals are
rankdeficient: see
qr
.  ...
 further arguments passed to or from other methods.
Details
The summary.manova
method uses a multivariate test statistic
for the summary table. Wilks' statistic is most popular in the
literature, but the default PillaiBartlett statistic is recommended
by Hand and Taylor (1987).
The table gives a transformation of the test statistic which has approximately an F distribution. The approximations used follow SPLUS and SAS (the latter apart from some cases of the HotellingLawley statistic), but many other distributional approximations exist: see Anderson (1984) and Krzanowski and Marriott (1994) for further references. All four approximate F statistics are the same when the term being tested has one degree of freedom, but in other cases that for the Roy statistic is an upper bound.
The tolerance tol
is applied to the QR decomposition of the
residual correlation matrix (unless some response has essentially zero
residuals, when it is unscaled). Thus the default value guards
against very highly correlated responses: it can be reduced but doing
so will allow rather inaccurate results and it will normally be better
to transform the responses to remove the high correlation.
Value

An object of class
 row.names
 The names of the terms, the row names of the
stats
table if present.  SS
 A named list of sums of squares and product matrices.
 Eigenvalues
 A matrix of eigenvalues.
 stats
 A matrix of the statistics, approximate F value, degrees of freedom and P value. otherwise components
"summary.manova"
. If there is a positive
residual degrees of freedom, this is a list with components
row.names
, SS
and Df
(degrees of freedom) for the terms (and not the residuals).
References
Anderson, T. W. (1994) An Introduction to Multivariate Statistical Analysis. Wiley.
Hand, D. J. and Taylor, C. C. (1987) Multivariate Analysis of Variance and Repeated Measures. Chapman and Hall.
Krzanowski, W. J. (1988) Principles of Multivariate Analysis. A User's Perspective. Oxford.
Krzanowski, W. J. and Marriott, F. H. C. (1994) Multivariate Analysis. Part I: Distributions, Ordination and Inference. Edward Arnold.