R/tukeyTest.R

In PMCMRplus: Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

## tukeyTest.R
## Part of the R package: PMCMRplus
##
## Copyright (C) 2017-2020 Thorsten Pohlert
##
##  This program is free software; you can redistribute it and/or modify
##  it under the terms of the GNU General Public License as published by
##  the Free Software Foundation; either version 3 of the License, or
##  (at your option) any later version.
##
##  This program is distributed in the hope that it will be useful,
##  but WITHOUT ANY WARRANTY; without even the implied warranty of
##  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
##  GNU General Public License for more details.
##
##  A copy of the GNU General Public License is available at
##  http://www.r-project.org/Licenses/

#' @name tukeyTest
#' @title Tukey's Multiple Comparison Test
#' @description
#' Performs Tukey's all-pairs comparisons test for normally distributed
#' data with equal group variances.
#' @details
#' For all-pairs comparisons in an one-factorial layout
#' with normally distributed residuals and equal variances
#' Tukey's test can be performed.
#' Let \eqn{X_{ij}} denote a continuous random variable
#' with the \eqn{j}-the realization (\eqn{1 \le j \le n_i})
#' in the \eqn{i}-th group (\eqn{1 \le i \le k}). Furthermore, the total
#' sample size is \eqn{N = \sum_{i=1}^k n_i}. A total of \eqn{m = k(k-1)/2}
#' hypotheses can be tested: The null hypothesis is
#' H\eqn{_{ij}: \mu_i = \mu_j ~~ (i \ne j)} is tested against the alternative
#' A\eqn{_{ij}: \mu_i \ne \mu_j} (two-tailed). Tukey's all-pairs test
#' statistics are given by
#'
#' \deqn{
#'  t_{ij} \frac{\bar{X}_i - \bar{X_j}}
#'  {s_{\mathrm{in}} \left(1/n_j + 1/n_i\right)^{1/2}}, ~~
#'  (i \ne j)
#' }{%
#'  SEE PDF
#' }
#'
#' with \eqn{s^2_{\mathrm{in}}} the within-group ANOVA variance.
#' The null hypothesis is rejected if \eqn{|t_{ij}| > q_{vm\alpha} / \sqrt{2}},
#' with \eqn{v = N - k} degree of freedom. The p-values are computed
#' from the \code{\link[stats]{Tukey}} distribution.
#'
#' @template class-PMCMR
#'
#' @references
#' Sachs, L. (1997) \emph{Angewandte Statistik}, New York: Springer.
#'
#' Tukey, J. (1949) Comparing Individual Means in the Analysis of Variance,
#' \emph{Biometrics} \bold{5}, 99--114.
#'
#' @keywords htest
#' @seealso
#' \code{\link{Tukey}}, \code{\link{TukeyHSD}}
#' @examples
#' fit <- aov(weight ~ feed, chickwts)
#' shapiro.test(residuals(fit))
#' bartlett.test(weight ~ feed, chickwts)
#' anova(fit)
#'
#' ## also works with fitted objects of class aov
#' res <- tukeyTest(fit)
#' summary(res)
#' summaryGroup(res)
#' @export
tukeyTest <- function(x, ...) UseMethod("tukeyTest")

#' @rdname tukeyTest
#' @aliases tukeyTest.default
#' @method tukeyTest default
#' @template one-way-parms-aov
#' @importFrom stats complete.cases
#' @importFrom stats var
#' @importFrom stats ptukey
#' @export
tukeyTest.default <- function(x, g, ...){
        ## taken from stats::kruskal.test

    if (is.list(x)) {
        if (length(x) < 2L)
            stop("'x' must be a list with at least 2 elements")
        DNAME <- deparse(substitute(x))
        x <- lapply(x, function(u) u <- u[complete.cases(u)])
        k <- length(x)
        l <- sapply(x, "length")
        if (any(l == 0))
            stop("all groups must contain data")
        g <- factor(rep(1 : k, l))
        x <- unlist(x)
    }
    else {
        if (length(x) != length(g))
            stop("'x' and 'g' must have the same length")
        DNAME <- paste(deparse(substitute(x)), "and",
                       deparse(substitute(g)))
        OK <- complete.cases(x, g)
        x <- x[OK]
        g <- g[OK]
        if (!all(is.finite(g)))
            stop("all group levels must be finite")
        g <- factor(g)
        k <- nlevels(g)
        if (k < 2)
            stop("all observations are in the same group")
    }

    ## prepare tukey test
    ni <- tapply(x, g, length)
    n <- sum(ni)
    xi <- tapply(x, g, mean)
    s2i <- tapply(x, g, var)
    s2in <- 1 / (n - k) * sum(s2i * (ni - 1))

    compare.stats <- function(i,j) {
        dif <- xi[i] - xi[j]
        A <- s2in * 0.5 * (1 / ni[i] + 1 / ni[j])
        qval <- dif / sqrt(A)
        return(qval)
    }

    PSTAT <- pairwise.table(compare.stats,levels(g), p.adjust.method="none" )
    PVAL <- ptukey(abs(PSTAT), nmeans = k, df = (n - k), lower.tail = FALSE)
    MODEL <- data.frame(x, g)
    DIST <- "q"
    METHOD <- "Tukey's test"
    ans <- list(method = METHOD, data.name = DNAME, p.value = PVAL,
                statistic = PSTAT, p.adjust.method = "single-step",
                model = MODEL, dist = DIST, alternative = "two.sided")
    class(ans) <- "PMCMR"
    ans
}

#' @rdname tukeyTest
#' @aliases tukeyTest.formula
#' @method tukeyTest formula
#' @template one-way-formula
#' @export
tukeyTest.formula <-
function(formula, data, subset, na.action, ...)
{
    mf <- match.call(expand.dots=FALSE)
    m <- match(c("formula", "data", "subset", "na.action"), names(mf), 0L)
    mf <- mf[c(1L, m)]
    mf[[1L]] <- quote(stats::model.frame)

    if(missing(formula) || (length(formula) != 3L))
        stop("'formula' missing or incorrect")
    mf <- eval(mf, parent.frame())
    if(length(mf) > 2L)
        stop("'formula' should be of the form response ~ group")
    DNAME <- paste(names(mf), collapse = " by ")
    names(mf) <- NULL
    y <- do.call("tukeyTest", c(as.list(mf)))
    y$data.name <- DNAME
    y
}

#' @rdname tukeyTest
#' @aliases tukeyTest.aov
#' @method tukeyTest aov
# @param obj A fitted model object, usually an \link[stats]{aov} fit.
#' @export
tukeyTest.aov <- function(x, ...) {
  model <- x$model
  DNAME <- paste(names(model), collapse = " by ")
  names(model) <- c("x", "g")
  y <- do.call("tukeyTest", as.list(model))
  y$data.name <- DNAME
  y
}