manova {base}R Documentation

Multivariate Analysis of Variance

Description

A class of multivariate analysis of variance and a summary method.

Usage

manova(...)
summary.manova(object,
               test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"),
               intercept = FALSE)

Arguments

... Arguments to be passed to aov
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.

Details

Class "manova" differs from class "aov" in selecting a different summary method. Function manova calls aov and then add class "manova" to the result object for each stratum.

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).

Value

A list with components

SS A names list of sums of squares and product matrices.
Eigenvalues A matrix of eigenvalues,
stats A matrix of the statistics, approximate F value and degrees of freedom.

Author(s)

B.D. Ripley

References

Krzanowski, W. J. (1988) Principles of Multivariate Analysis. A User's Perspective. Oxford.

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

See Also

aov

Examples

## Example on producing plastic filem 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