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## cuzickTest.R
##
## 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 cuzickTest
#' @title Testing against Ordered Alternatives (Cuzick's Test)
#' @description
#' Performs Cuzick's test for testing against ordered alternatives.
#'
#' @details
#' The null hypothesis, H\eqn{_0: \theta_1 = \theta_2 = \ldots = \theta_k}
#' is tested against a simple order hypothesis,
#' H\eqn{_\mathrm{A}: \theta_1 \le \theta_2 \le \ldots \le
#' \theta_k,~\theta_1 < \theta_k}.
#'
#' The p-values are estimated from the standard normal distribution.
#'
#' @template class-htest
#' @template trendTests
#' @references
#' Cuzick, J. (1995) A Wilcoxon-type test for trend, \emph{Statistics in Medicine}
#' \bold{4}, 87--90.
#'
#' @concept wilcoxonranks
#' @export cuzickTest
cuzickTest <- function(x, ...) UseMethod("cuzickTest")
#' @rdname cuzickTest
#' @method cuzickTest default
#' @aliases cuzickTest.default
#' @template one-way-parms
#' @param alternative the alternative hypothesis. Defaults to \code{"two.sided"}.
#' @param scores numeric vector of scores. Defaults to \code{NULL}.
#' @param continuity logical indicator whether a continuity correction
#' shall be performed. Defaults to \code{FALSE}.
#' @importFrom stats pnorm complete.cases
#' @export
cuzickTest.default <-
function(x, g, alternative = c("two.sided", "greater", "less"),
scores = NULL, continuity = FALSE, ...)
{
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))
if(!is.null(x$alternative)) alternative <- x$alternative
if(is.null(x$continuity)) {
continuity <- FALSE
} else {
continuity <- TRUE
}
if(is.null(x$scores)) {
scores <- NULL
} else {
scores <- x$scores
}
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")
}
alternative <- match.arg(alternative)
n <- length(x)
if (n < 2)
stop("not enough observations")
ni <- tapply(x, g, length)
rx <- rank(x)
## check for ties
TIES <- FALSE
TIES <- sum(table(rx) - 1) != 0
if(TIES){
warning("Ties are present. 'cuzickTest()' does not correct for ties")
}
Ri <- tapply(rx, g, sum)
if(is.null(scores)) {
li <- 1:k
} else {
if (!is.numeric(scores) | length(scores) != k){
stop("'scores' must be a numeric vector with 'length == nr of groups'")
} else {
li <- scores
}
}
T <- sum(Ri * li)
L <- sum(ni * li)
eT <- L * (n + 1) / 2
varT <- ((n + 1) / 12) * (n * sum(li^2 * ni) - L^2)
if (!continuity) {
STAT <- (T - eT) / sqrt(varT)
} else {
if (T > eT){
STAT <- (T - eT - 0.5) / sqrt(varT)
} else {
STAT <- (T - eT + 0.5) / sqrt(varT)
}
}
ESTIMATE <- T
if (alternative == "two.sided"){
PVAL <- 2 * min(pnorm(abs(STAT), lower.tail = FALSE), 0.5)
} else if (alternative == "greater"){
PVAL <- pnorm(STAT, lower.tail = FALSE)
} else {
PVAL <- pnorm(STAT)
}
names(STAT) <- "z"
names(ESTIMATE) <- "CU"
RVAL <- list(statistic = STAT,
p.value = PVAL,
method = "Cuzick trend test",
data.name = DNAME,
alternative = alternative,
estimate = ESTIMATE)
class(RVAL) <- "htest"
return(RVAL)
}
#' @rdname cuzickTest
#' @method cuzickTest formula
#' @aliases cuzickTest.formula
#' @template one-way-formula
#' @export
cuzickTest.formula <-
function(formula, data, subset, na.action,
alternative = c("two.sided", "greater", "less"),
scores = NULL, continuity = FALSE, ...)
{
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 ")
alternative <- match.arg(alternative)
if(is.null(scores)) scores <- NULL
names(mf) <- NULL
y <- do.call("cuzickTest", c(as.list(mf), alternative = alternative,
scores = scores, continuity = continuity))
y$data.name <- DNAME
y
}
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