R/frdAllPairsSiegelTest.R

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

## frdAllPairsSiegelTest.R
## Part of the R package: PMCMR
##
## 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/

#' @rdname frdAllPairsSiegelTest
#' @title Siegel and Castellan's All-Pairs Comparisons Test for
#' Unreplicated Blocked Data
#' @description
#'  Performs Siegel and Castellan's all-pairs comparisons tests
#' of Friedman-type ranked data.
#' @details
#' For all-pairs comparisons in a two factorial unreplicated
#' complete block design
#' with non-normally distributed residuals, Siegel and Castellan's test can be
#' performed on Friedman-type ranked data.
#'
#' A total of \eqn{m = k ( k -1 )/2} hypotheses can be tested.
#' The null hypothesis, H\eqn{_{ij}: \theta_i = \theta_j}, is tested
#' in the two-tailed case against the alternative,
#' A\eqn{_{ij}: \theta_i \ne \theta_j, ~~ i \ne j}.
#'
#' The \eqn{p}-values are computed from the standard normal distribution.
#' Any method as implemented in \code{\link{p.adjust}} can be used for
#' \code{p}-value adjustment.
#'
#' @references
#' Siegel, S., Castellan Jr., N. J. (1988) \emph{Nonparametric
#'    Statistics for the Behavioral Sciences}. 2nd ed. New York: McGraw-Hill.
#'
#' @keywords htest nonparametric
#' @concept friedmanranks
#' @seealso
#' \code{\link{friedmanTest}}, \code{\link{friedman.test}},
#' \code{\link{frdAllPairsExactTest}}, \code{\link{frdAllPairsConoverTest}},
#' \code{\link{frdAllPairsNemenyiTest}}, \code{\link{frdAllPairsMillerTest}}
#' @template class-PMCMR
#' @example examples/frdAllPairs.R
#' @export
frdAllPairsSiegelTest <-
    function(y, ...) UseMethod("frdAllPairsSiegelTest")

#' @rdname frdAllPairsSiegelTest
#' @aliases frdAllPairsSiegelTest.default
#' @method frdAllPairsSiegelTest default
#' @template two-way-parms
#' @param p.adjust.method method for adjusting p values
#'    (see \code{\link{p.adjust}}).
#' @importFrom stats pnorm
#' @export
frdAllPairsSiegelTest.default <-
    function(y, groups, blocks, p.adjust.method = p.adjust.methods, ...)
{
    p.adjust.method <- match.arg(p.adjust.method)
    ## 2019-10-16
    ## novel external function
    ans <- frdRanks(y, groups, blocks)
    r <- ans$r
    n <- nrow(r)
    k <- ncol(r)
    GRPNAMES <- colnames(r)

    R.mnsum <- colMeans(r)

    compare.stats <- function(i,j) {
        dif <- abs(R.mnsum[i] - R.mnsum[j])
        zval <- dif / sqrt(k * (k + 1) / (6 * n))
        return(zval)
    }

    ## z value
    METHOD <- c("Siegel-Castellan all-pairs test for a two-way",
               " balanced complete block design")
    PSTAT <- pairwise.table(compare.stats,
                            GRPNAMES, p.adjust.method="none")
    pstat <- as.numeric(PSTAT)
    pval <- 2 * pnorm(abs(pstat), lower.tail = FALSE)
    pval[pval > 1] <- 1.0
    padj <- p.adjust(pval, method = p.adjust.method)
    PVAL <- matrix(padj, ncol = (k - 1), nrow = (k -1 ))
    DIST <- "z"

    colnames(PSTAT) <- GRPNAMES[1:(k-1)]
    rownames(PSTAT) <- GRPNAMES[2:k]
    colnames(PVAL) <- GRPNAMES[1:(k-1)]
    rownames(PVAL) <- GRPNAMES[2:k]

    ans <- list(method = METHOD,
                data.name = ans$DNAME,
                p.value = PVAL,
                statistic = PSTAT,
                p.adjust.method = p.adjust.method,
                dist = DIST,
                model = ans$inDF)
    class(ans) <- "PMCMR"
    ans
}