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\name{fourfoldplot}
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\alias{fourfoldplot}
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\title{Fourfold Plots}
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\description{
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Creates a fourfold display of a 2 by 2 by \eqn{k} contingency table on
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the current graphics device, allowing for the visual inspection of the
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association between two dichotomous variables in one or several
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populations (strata).
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}
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\usage{
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fourfoldplot(x, color = c("#99CCFF", "#6699CC"), conf.level = 0.95,
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std = c("margins", "ind.max", "all.max"),
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margin = c(1, 2), space = 0.2, main = NULL,
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mfrow = NULL, mfcol = NULL)
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}
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\arguments{
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\item{x}{a 2 by 2 by \eqn{k} contingency table in array form, or as a
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2 by 2 matrix if \eqn{k} is 1.}
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\item{color}{a vector of length 2 specifying the colors to use for the
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smaller and larger diagonals of each 2 by 2 table.}
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\item{conf.level}{confidence level used for the confidence rings on
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the odds ratios. Must be a single nonnegative number less than 1;
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if set to 0, confidence rings are suppressed.}
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\item{std}{a character string specifying how to standardize the table.
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Must be one of \code{"margins"}, \code{"ind.max"}, or
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\code{"all.max"}, and can be abbreviated by the initial letter.
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If set to \code{"margins"}, each 2 by 2 table is standardized to
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equate the margins specified by \code{margin} while preserving the
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odds ratio. If \code{"ind.max"} or \code{"all.max"}, the tables are
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either individually or simultaneously standardized to a maximal cell
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frequency of 1.}
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\item{margin}{a numeric vector with the margins to equate. Must be
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one of \code{1}, \code{2}, or \code{c(1, 2)} (the default), which
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corresponds to standardizing the row, column, or both margins in
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each 2 by 2 table.
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Only used if \code{std} equals \code{"margins"}.}
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\item{space}{the amount of space (as a fraction of the maximal radius
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of the quarter circles) used for the row and column lebals.}
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\item{main}{character string for the fourfold title.}
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\item{mfrow}{a numeric vector of the form \code{c(nr, nc)}, indicating
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that the displays for the 2 by 2 tables should be arranged in an
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\code{nr} by \code{nc} layout, filled by rows.}
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\item{mfcol}{a numeric vector of the form \code{c(nr, nc)}, indicating
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that the displays for the 2 by 2 tables should be arranged in an
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\code{nr} by \code{nc} layout, filled by columns.}
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}
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\details{
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The fourfold display is designed for the display of 2 by 2 by \eqn{k}
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tables.
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Following suitable standardization, the cell frequencies
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\eqn{f_{ij}}{f[i,j]} of each 2 by 2 table are shown as a quarter
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circle whose radius is proportional to
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\eqn{\sqrt{f_{ij}}}{sqrt(f[i,j])} so that its area is proportional to
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the cell frequency. An association (odds ratio different from 1)
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between the binary row and column variables is indicated by the
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tendency of diagonally opposite cells in one direction to differ in
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size from those in the other direction; color is used to show this
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direction. Confidence rings for the odds ratio allow a visual test of
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the null of no association; the rings for adjacent quadrants overlap
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iff the observed counts are consistent with the null hypothesis.
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Typically, the number \eqn{k} corresponds to the number of levels of a
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stratifying variable, and it is of interest to see whether the
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association is homogeneous across strata. The fourfold display
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visualizes the pattern of association. Note that the confidence rings
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for the individual odds ratios are not adjusted for multiple testing.
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}
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\references{
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Friendly, M. (1994).
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A fourfold display for 2 by 2 by \eqn{k} tables.
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Technical Report 217, York University, Psychology Department.
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\url{http://www.math.yorku.ca/SCS/Papers/4fold/4fold.ps.gz}
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}
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\seealso{
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\code{\link{mosaicplot}}
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}
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\examples{
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data(UCBAdmissions)
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## Use the Berkeley admission data as in Friendly (1995).
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x <- aperm(UCBAdmissions, c(2, 1, 3))
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dimnames(x)[[2]] <- c("Yes", "No")
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names(dimnames(x)) <- c("Sex", "Admit?", "Department")
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stats::ftable(x)
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## Fourfold display of data aggregated over departments, with
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## frequencies standardized to equate the margins for admission
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## and sex.
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## Figure 1 in Friendly (1994).
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fourfoldplot(margin.table(x, c(1, 2)))
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## Fourfold display of x, with frequencies in each table
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## standardized to equate the margins for admission and sex.
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## Figure 2 in Friendly (1994).
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fourfoldplot(x)
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## Fourfold display of x, with frequencies in each table
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## standardized to equate the margins for admission. but not
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## for sex.
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## Figure 3 in Friendly (1994).
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fourfoldplot(x, margin = 2)
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}
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\keyword{hplot}
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