Summary Method for Multivariate Analysis of Variance
summary method for class
## S3 method for class 'manova': summary(object, test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"), intercept = FALSE, tol = 1e-7, ...)
- An object of class
aovobject with multiple responses.
- The name of the test statistic to be used. Partial matching is used so the name can be abbreviated.
- logical. If
TRUE, the intercept term is included in the table.
- tolerance to be used in deciding if the residuals are
- further arguments passed to or from other methods.
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.
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.
- An object of class
"summary.manova". If there is a positive residual degrees of freedom, this is a list with components
row.names The names of the terms, the row names of the
statstable 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
Df(degrees of freedom) for the terms (and not the residuals).
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 <- gl(2,10, labels = c("Low", "High")) additive <- gl(2, 5, length = 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