The R Project SVN R

% File src/library/graphics/man/fourfoldplot.Rd

% Part of the R package, https://www.R-project.org

% Copyright 1995-2025 R Core Team

% Distributed under GPL 2 or later

\name{fourfoldplot}

\alias{fourfoldplot}

\title{Fourfold Plots}

\description{

  Creates a fourfold display of a 2 by 2 by \eqn{k} contingency table on

  the current graphics device, allowing for the visual inspection of the

  association between two dichotomous variables in one or several

  populations (strata).

}

\usage{

fourfoldplot(x, color = c("#99CCFF", "#6699CC"),

             conf.level = 0.95,

             std = c("margins", "ind.max", "all.max"),

             margin = c(1, 2), space = 0.2, main = NULL,

             mfrow = NULL, mfcol = NULL)

}

\arguments{

  \item{x}{a 2 by 2 by \eqn{k} contingency table in array form, or as a

    2 by 2 matrix if \eqn{k} is 1.}

  \item{color}{a vector of length 2 specifying the colors to use for the

    smaller and larger diagonals of each 2 by 2 table.}

  \item{conf.level}{confidence level used for the confidence rings on

    the odds ratios.  Must be a single nonnegative number less than 1;

    if set to 0, confidence rings are suppressed.}

  \item{std}{a character string specifying how to standardize the table.

    Must match one of \code{"margins"}, \code{"ind.max"}, or

    \code{"all.max"}, and can be abbreviated to the initial letter.

    If set to \code{"margins"}, each 2 by 2 table is standardized to

    equate the margins specified by \code{margin} while preserving the

    odds ratio.  If \code{"ind.max"} or \code{"all.max"}, the tables are

    either individually or simultaneously standardized to a maximal cell

    frequency of 1.}

  \item{margin}{a numeric vector with the margins to equate.  Must be

    one of \code{1}, \code{2}, or \code{c(1, 2)} (the default), which

    corresponds to standardizing the row, column, or both margins in

    each 2 by 2 table.

    Only used if \code{std} equals \code{"margins"}.}

  \item{space}{the amount of space (as a fraction of the maximal radius

    of the quarter circles) used for the row and column labels.}

  \item{main}{character string for the fourfold title.}

  \item{mfrow}{a numeric vector of the form \code{c(nr, nc)}, indicating

    that the displays for the 2 by 2 tables should be arranged in an

    \code{nr} by \code{nc} layout, filled by rows.}

  \item{mfcol}{a numeric vector of the form \code{c(nr, nc)}, indicating

    that the displays for the 2 by 2 tables should be arranged in an

    \code{nr} by \code{nc} layout, filled by columns.}

}

\details{

  The fourfold display is designed for the display of 2 by 2 by \eqn{k}

  tables.

  Following suitable standardization, the cell frequencies

  \eqn{f_{ij}}{f[i,j]} of each 2 by 2 table are shown as a quarter

  circle whose radius is proportional to

  \eqn{\sqrt{f_{ij}}}{sqrt(f[i,j])} so that its area is proportional to

  the cell frequency.  An association (odds ratio different from 1)

  between the binary row and column variables is indicated by the

  tendency of diagonally opposite cells in one direction to differ in

  size from those in the other direction; color is used to show this

  direction.  Confidence rings for the odds ratio allow a visual test of

  the null of no association; the rings for adjacent quadrants overlap

  if and only if the observed counts are consistent with the null hypothesis.

  Typically, the number \eqn{k} corresponds to the number of levels of a

  stratifying variable, and it is of interest to see whether the

  association is homogeneous across strata.  The fourfold display

  visualizes the pattern of association.  Note that the confidence rings

  for the individual odds ratios are not adjusted for multiple testing.

}

\references{

  \bibshow{R:Friendly:1994b}

}

\seealso{

  \code{\link{mosaicplot}}

}

\examples{

## Use the Berkeley admission data as in Friendly (1994).

x <- aperm(UCBAdmissions, c(2, 1, 3))

dimnames(x)[[2]] <- c("Yes", "No")

names(dimnames(x)) <- c("Sex", "Admit?", "Department")

stats::ftable(x)

## Fourfold display of data aggregated over departments, with

## frequencies standardized to equate the margins for admission

## and sex.

## Figure 1 in Friendly (1994).

fourfoldplot(marginSums(x, c(1, 2)))

## Fourfold display of x, with frequencies in each table

## standardized to equate the margins for admission and sex.

## Figure 2 in Friendly (1994).

fourfoldplot(x)

## Fourfold display of x, with frequencies in each table

## standardized to equate the margins for admission. but not

## for sex.

## Figure 3 in Friendly (1994).

fourfoldplot(x, margin = 2)

}

\keyword{hplot}