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## snkTest.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 snkTest
#' @title Student-Newman-Keuls Test
#' @description
#' Performs Student-Newman-Keuls 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
#' Student-Newman-Keuls test can be performed. A total of \eqn{m = k(k-1)/2}
#' hypotheses can be tested. The null hypothesis
#' H\eqn{_{ij}: \mu_i(x) = \mu_j(x)} is tested in the two-tailed test
#' against the alternative
#' A\eqn{_{ij}: \mu_i(x) \ne \mu_j(x), ~~ i \ne j}.
#'
#' The p-values are computed from the Tukey-distribution.
#'
#' @template class-PMCMR
#'
#' @references
#' Keuls, M. (1952) The use of the "studentized range"
#' in connection with an analysis of variance,
#' \emph{Euphytica} \bold{1}, 112--122.
#'
#' Newman, D. (1939) The distribution of range in
#' samples from a normal population, expressed in
#' terms of an independent estimate of standard
#' deviation, \emph{Biometrika} \bold{31}, 20--30.
#'
#' Student (1927) Errors of routine analysis,
#' \emph{Biometrika} \bold{19}, 151--164.
#'
#' @keywords htest
#' @seealso
#' \code{\link[stats]{Tukey}}, \code{\link[stats]{TukeyHSD}} \code{\link{tukeyTest}}
#' @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 <- snkTest(fit)
#' summary(res)
#' summaryGroup(res)
#' @export
snkTest <- function(x, ...) UseMethod("snkTest")
#' @rdname snkTest
#' @aliases snkTest.default
#' @method snkTest default
#' @template one-way-parms-aov
#' @importFrom stats complete.cases
#' @importFrom stats var
#' @importFrom stats ptukey
#' @export
snkTest.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 snk-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))
df <- n -k
## order means
o <- order(xi, decreasing = TRUE)
levNames <- levels(g)
qval <- matrix(NA, ncol = k-1, nrow = k-1)
colnames(qval) <- levNames[1:(k - 1)]
rownames(qval) <- levNames[2:k]
pval <- qval
for (j in 1:(k-1)) {
for (i in (j+1):k){
qval[i-1, j] <- (xi[i] - xi[j]) /
sqrt((s2in / 2) * (1 / ni[i] + 1 / ni[j]))
p <- 1 + abs(which(o == i, arr.ind = TRUE) -
which(o == j, arr.ind = TRUE))
pval[i-1, j] <- ptukey(q = abs(qval[i-1, j]),
nmeans = p,
df = df,
lower.tail = FALSE)
}
}
MODEL <- data.frame(x, g)
DIST <- "q"
METHOD <- "SNK test"
ans <- list(method = METHOD, data.name = DNAME, p.value = pval,
statistic = qval, p.adjust.method = "step down",
model = MODEL, dist = DIST, alternative = "two.sided")
class(ans) <- "PMCMR"
ans
}
#' @rdname snkTest
#' @aliases snkTest.formula
#' @method snkTest formula
#' @template one-way-formula
#' @export
snkTest.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("snkTest", c(as.list(mf)))
y$data.name <- DNAME
y
}
#' @rdname snkTest
#' @aliases snkTest.aov
#' @method snkTest aov
# @param obj A fitted model object, usually an \link[stats]{aov} fit.
#' @export
snkTest.aov <- function(x, ...) {
model <- x$model
DNAME <- paste(names(model), collapse = " by ")
names(model) <- c("x", "g")
y <- do.call("snkTest", as.list(model))
y$data.name <- DNAME
y
}
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