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\name{xtabs}\alias{xtabs}\alias{print.xtabs}\title{Cross Tabulation}\description{Create a contingency table from cross-classifying factors, usuallycontained in a data frame, using a formula interface.}\usage{xtabs(formula = ~., data, subset, na.action, exclude = c(NA, NaN),drop.unused.levels = FALSE)}\arguments{\item{formula}{a formula object with the cross-classifying variables,separated by \code{+}, on the right hand side. Interactions are notallowed. On the left hand side, one may optionally give a vector ora matrix of counts; in the latter case, the columns are interpretedas corresponding to the levels of a variable. This is useful if thedata has already beed tabulated, see the examples below.}\item{data}{a data frame, list or environment containing the variablesto be cross-tabulated.}\item{subset}{an optional vector specifying a subset of observationsto be used.}\item{na.action}{a function which indicates what should happen whenthe data contain \code{NA}s.}\item{exclude}{a vector of values to be excluded when forming theset of levels of the classifying factors.}\item{drop.unused.levels}{a logical indicating whether to drop unusedlevels in the classifying factors. If this is \code{FALSE} andthere are unused levels, the table will contain zero marginals, anda subsequent chi-squared test for independence of the factors willnot work.}}\details{There is a \code{summary} method for contingency table objects createdby \code{table} or \code{xtabs}, which gives basic information andperforms a chi-squared test for independence of factors (note that thefunction \code{\link[ctest]{chisq.test}} in package \bold{ctest}currently only handles 2-d tables).}\value{A contingency table in array representation of class \code{c("xtabs","table")}, with a \code{"call"} attribute storing the matched call.}\seealso{\code{\link{table}} for ``traditional'' cross-tabulation, and\code{\link{as.data.frame.table}} which is the inverse operation of\code{xtabs} (see the \code{DF} example below).}\examples{data(esoph)## `esoph' has the frequencies of cases and controls for all levels of## the variables `agegp', `alcgp', and `tobgp'.xtabs(cbind(ncases, ncontrols) ~ ., data = esoph)## Output is not really helpful ... flat tables are better:ftable(xtabs(cbind(ncases, ncontrols) ~ ., data = esoph))## In particular if we have fewer factors ...ftable(xtabs(cbind(ncases, ncontrols) ~ agegp, data = esoph))data(UCBAdmissions)## This is already a contingency table in array form.DF <- as.data.frame(UCBAdmissions)## Now `DF' is a data frame with a grid of the factors and the counts## in variable `Freq'.DF## Nice for taking margins ...xtabs(Freq ~ Gender + Admit, DF)## And for testing independece ...summary(xtabs(Freq ~ ., DF))}\keyword{category}