| summary.manova {stats} | R Documentation |
A summary method for class "manova".
## S3 method for class 'manova':
summary(object,
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.
## 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