swh:1:snp:813359ba77493c9d5dd1abad9a1f53490a8abf57
Tip revision: cd5ace5b6355edbcf1277dc2a8cb00999df6f943 authored by Torsten Hothorn on 29 September 2009, 00:00:00 UTC
version 1.0-7
version 1.0-7
Tip revision: cd5ace5
MarginalHomogeneityTest.Rd
\name{MarginalHomogeneityTest}
\alias{mh_test}
\alias{mh_test.table}
\alias{mh_test.formula}
\alias{mh_test.SymmetryProblem}
\title{ Marginal Homogeneity Test }
\description{
Testing marginal homogeneity in a complete block design.
}
\usage{
\method{mh_test}{formula}(formula, data, subset = NULL, \dots)
\method{mh_test}{table}(object, ...)
\method{mh_test}{SymmetryProblem}(object, distribution = c("asymptotic", "approximate"), ...)
}
\arguments{
\item{formula}{a formula of the form \code{y ~ x | block} where \code{y}
is a factor giving the data values and
\code{x} a factor with two or more levels giving the corresponding
replications. \code{block} is an
optional factor (which is generated automatically when omitted).}
\item{data}{an optional data frame containing the variables in the
model formula.}
\item{subset}{an optional vector specifying a subset of observations
to be used.}
\item{object}{an object inheriting from class \code{SymmetryProblem} or a
\code{table} with identical \code{dimnames} attributes.}
\item{distribution}{a character, the null distribution of the test statistic
can be approximated by its asymptotic distribution (\code{asymptotic})
or via Monte-Carlo resampling (\code{approximate}).
Alternatively, the functions
\code{\link{approximate}} or \code{\link{asymptotic}} can be
used to specify how the exact conditional distribution of the test statistic
should be calculated or approximated.}
\item{\dots}{further arguments to be passed to or from methods.}
}
\details{
The null hypothesis of independence of row and column totals is tested.
The corresponding test for binary factors \code{x} and \code{y} is known
as McNemar test. For larger tables, Stuart's \eqn{W_0}
statistic (Stuart, 1955, Agresti, 2002, page 422, also known as Stuart-Maxwell test)
is computed. The marginal homogeneity
statistic \eqn{W} of Bhapkar (1966) can be derived from \eqn{W_0}
via \eqn{W = W_0 / (1 - W_0 / n)} (see Agresti, 2002, page 422).
Scores must be a list of length one (row and column scores coincide). When
scores are given or if \code{x} is ordered, the corresponding
linear association test is computed (see Agresti, 2002).
Note that for a large number of observations, this function
is rather inefficient.
}
\value{
An object inheriting from class \code{IndependenceTest} with
methods \code{show}, \code{pvalue} and \code{statistic}.
}
\references{
Alan Agresti (2002). \emph{Categorical Data Analysis}. Hoboken, New
Jersey: John Wiley & Sons.
V. P. Bhapkar (1966). A note on the equivalence of two test criteria for hypotheses
in categorical data. \emph{Journal of the American Statistical Association} \bold{61},
228--235.
Alan Stuart (1955). A test for homogeneity of the marginal distributions in a two-way
classification. \emph{Biometrika} \bold{42}(3/4), 412--416.
}
\examples{
### Opinions on Pre- and Extramarital Sex, Agresti (2002), page 421
opinions <- c("always wrong", "almost always wrong",
"wrong only sometimes", "not wrong at all")
PreExSex <- as.table(matrix(c(144, 33, 84, 126,
2, 4, 14, 29,
0, 2, 6, 25,
0, 0, 1, 5), nrow = 4,
dimnames = list(PremaritalSex = opinions,
ExtramaritalSex = opinions)))
### treating response as nominal
mh_test(PreExSex)
### and as ordinal
mh_test(PreExSex, scores = list(response = 1:length(opinions)))
### example taken from
### http://ourworld.compuserve.com/homepages/jsuebersax/mcnemar.htm
rating <- c("low", "moderate", "high")
x <- as.table(matrix(c(20, 10, 5,
3, 30, 15,
0, 5, 40),
ncol = 3, byrow = TRUE,
dimnames = list(Rater1 = rating, Rater2 = rating)))
### test statistic W_0 = 13.76
mh_test(x)
}
\keyword{htest}