| % File src/library/stats/man/summary.manova.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2008 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{summary.manova} |
| \alias{summary.manova} |
| \alias{print.summary.manova} |
| \title{Summary Method for Multivariate Analysis of Variance} |
| \description{ |
| A \code{summary} method for class \code{"manova"}. |
| } |
| \usage{ |
| \method{summary}{manova}(object, |
| test = c("Pillai", "Wilks", "Hotelling-Lawley", "Roy"), |
| intercept = FALSE, tol = 1e-7, \dots) |
| } |
| \arguments{ |
| \item{object}{An object of class \code{"manova"} or an \code{aov} |
| object with multiple responses.} |
| \item{test}{The name of the test statistic to be used. Partial |
| matching is used so the name can be abbreviated.} |
| \item{intercept}{logical. If \code{TRUE}, the intercept term is |
| included in the table.} |
| \item{tol}{tolerance to be used in deciding if the residuals are |
| rank-deficient: see \code{\link{qr}}.} |
| \item{\dots}{further arguments passed to or from other methods.} |
| } |
| \details{ |
| The \code{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 \code{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. |
| } |
| \value{ |
| An object of class \code{"summary.manova"}. If there is a positive |
| residual degrees of freedom, this is a list with components |
| \item{row.names}{The names of the terms, the row names of the |
| \code{stats} table if present.} |
| \item{SS}{A named list of sums of squares and product matrices.} |
| \item{Eigenvalues}{A matrix of eigenvalues.} |
| \item{stats}{A matrix of the statistics, approximate F value, |
| degrees of freedom and P value.} |
| otherwise components \code{row.names}, \code{SS} and \code{Df} |
| (degrees of freedom) for the terms (and not the residuals). |
| } |
| \references{ |
| Anderson, T. W. (1994) \emph{An Introduction to Multivariate |
| Statistical Analysis.} Wiley. |
| |
| Hand, D. J. and Taylor, C. C. (1987) |
| \emph{Multivariate Analysis of Variance and Repeated Measures.} |
| Chapman and Hall. |
| |
| Krzanowski, W. J. (1988) \emph{Principles of Multivariate Analysis. A |
| User's Perspective.} Oxford. |
| |
| Krzanowski, W. J. and Marriott, F. H. C. (1994) \emph{Multivariate |
| Analysis. Part I: Distributions, Ordination and Inference.} Edward Arnold. |
| } |
| \seealso{ |
| \code{\link{manova}}, \code{\link{aov}} |
| } |
| |
| \examples{\donttest{ |
| ## 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 |
| }} |
| \keyword{models} |