summary method for class "manova".# S3 method for manova
summary(object,
test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
intercept = FALSE, tol = 1e-7, …)"manova" or an aov
object with multiple responses.TRUE, the intercept term is
included in the table.qr."summary.manova". If there is a positive
residual degrees of freedom, this is a list with components
stats table if present.row.names, SS and Df
(degrees of freedom) for the terms (and not the residuals).summary.manova method uses a multivariate test statistic
for the summary table. Wilks' statistic is most popular in the
literature, but the default Pillai--Bartlett 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
S-PLUS and SAS (the latter apart from some cases of the
Hotelling--Lawley 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.manova, aov