summary.manova {stats}R Documentation

Summary Method for Multivariate Analysis of Variance


A summary method for class "manova".


## S3 method for class 'manova':
        test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
        intercept = FALSE, ...)


object An object of class "manova" or an aov 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.
... further arguments passed to or from other methods.


The 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.


A list with components

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.


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.

See Also

manova, aov


## Example on producing plastic film from Krzanowski (1998, p. 381)
tear <- c(6.5, 6.2, 5.8, 6.5, 6.5, 6.9, 7.2, 6.9, 6.1, 6.3,
          6.7, 6.6, 7.2, 7.1, 6.8, 7.1, 7.0, 7.2, 7.5, 7.6)
gloss <- c(9.5, 9.9, 9.6, 9.6, 9.2, 9.1, 10.0, 9.9, 9.5, 9.4,
           9.1, 9.3, 8.3, 8.4, 8.5, 9.2, 8.8, 9.7, 10.1, 9.2)
opacity <- c(4.4, 6.4, 3.0, 4.1, 0.8, 5.7, 2.0, 3.9, 1.9, 5.7,
             2.8, 4.1, 3.8, 1.6, 3.4, 8.4, 5.2, 6.9, 2.7, 1.9)
Y <- cbind(tear, gloss, opacity)
rate <- factor(gl(2,10), labels=c("Low", "High"))
additive <- factor(gl(2, 5, len=20), labels=c("Low", "High"))

fit <- manova(Y ~ rate * additive)
summary.aov(fit)           # univariate ANOVA tables
summary(fit, test="Wilks") # ANOVA table of Wilks' lambda
summary(fit)               # same F statistics as single-df terms

[Package stats version 2.5.0 Index]