#  File src/library/stats/R/prop.test.R
#  Part of the R package, http://www.R-project.org
#
#  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 2 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/

prop.test <-
function(x, n, p = NULL, alternative = c("two.sided", "less", "greater"),
         conf.level = 0.95, correct = TRUE)
{
    DNAME <- deparse(substitute(x))

    if (is.table(x) && length(dim(x)) == 1L) {
        if (dim(x) != 2L)
            stop("table 'x' should have 2 entries")
        l <- 1
        n <- sum(x)
        x <- x[1L]
    }
    else if (is.matrix(x)) {
	if (ncol(x) != 2L)
	    stop("'x' must have 2 columns")
	l <- nrow(x)
	n <- rowSums(x)
	x <- x[, 1L]
    }
    else {
	DNAME <- paste(DNAME, "out of", deparse(substitute(n)))
	if ((l <- length(x)) != length(n))
	    stop("'x' and 'n' must have the same length")
    }

    OK <- complete.cases(x, n)
    x <- x[OK]
    n <- n[OK]
    if ((k <- length(x)) < 1L)
	stop("not enough data")
    if (any(n <= 0))
	stop("elements of 'n' must be positive")
    if (any(x < 0))
	stop("elements of 'x' must be nonnegative")
    if (any(x > n))
	stop("elements of 'x' must not be greater than those of 'n'")

    if (is.null(p) && (k == 1))
	p <- .5
    if (!is.null(p)) {
	DNAME <- paste(DNAME, ", null ",
		       ifelse(k == 1, "probability ", "probabilities "),
		       deparse(substitute(p)), sep = "")
	if (length(p) != l)
	    stop("'p' must have the same length as 'x' and 'n'")
	p <- p[OK]
	if (any((p <= 0) | (p >= 1)))
	    stop("elements of 'p' must be in (0,1)")
    }

    alternative <- match.arg(alternative)
    if (k > 2 || (k == 2) && !is.null(p))
	alternative <- "two.sided"

    if ((length(conf.level) != 1L) || is.na(conf.level) ||
	(conf.level <= 0) || (conf.level >= 1))
	stop("'conf.level' must be a single number between 0 and 1")

    correct <- as.logical(correct)

    ESTIMATE <- x/n
    names(ESTIMATE) <- if (k == 1) "p" else paste("prop", 1L:l)[OK]
    NVAL <- p
    CINT <- NULL
    YATES <- ifelse(correct && (k <= 2), .5, 0)

    if (k == 1) {
	z <- ifelse(alternative == "two.sided",
		    qnorm((1 + conf.level) / 2),
		    qnorm(conf.level))
	YATES <- min(YATES, abs(x - n * p))
        z22n <- z^2 / (2 * n)
	p.c <- ESTIMATE + YATES / n
	p.u <- if(p.c >= 1) 1 else (p.c + z22n
                  + z * sqrt(p.c * (1 - p.c) / n + z22n / (2 * n))) / (1+2*z22n)
	p.c <- ESTIMATE - YATES / n
	p.l <- if(p.c <= 0) 0 else (p.c + z22n
                  - z * sqrt(p.c * (1 - p.c) / n + z22n / (2 * n))) / (1+2*z22n)
	CINT <- switch(alternative,
		       "two.sided" = c(max(p.l, 0), min(p.u, 1)),
		       "greater" = c(max(p.l, 0), 1),
		       "less" = c(0, min(p.u, 1)))
    }
    else if ((k == 2) & is.null(p)) {
	DELTA <- ESTIMATE[1L] - ESTIMATE[2L]
	YATES <- min(YATES, abs(DELTA) / sum(1/n))
	WIDTH <- (switch(alternative,
			 "two.sided" = qnorm((1 + conf.level) / 2),
			 qnorm(conf.level))
		  * sqrt(sum(ESTIMATE * (1 - ESTIMATE) / n))
		  + YATES * sum(1/n))
	CINT <- switch(alternative,
		       "two.sided" = c(max(DELTA - WIDTH, -1),
		       min(DELTA + WIDTH, 1)),
		       "greater" = c(max(DELTA - WIDTH, -1), 1),
		       "less" = c(-1, min(DELTA + WIDTH, 1)))
    }
    if (!is.null(CINT))
	attr(CINT, "conf.level") <- conf.level

    METHOD <- paste(ifelse(k == 1,
			   "1-sample proportions test",
			   paste(k, "-sample test for ",
				 ifelse(is.null(p), "equality of", "given"),
				 " proportions", sep = "")),
		    ifelse(YATES, "with", "without"),
		    "continuity correction")

    if (is.null(p)) {
	p <- sum(x)/sum(n)
	PARAMETER <- k - 1
    }
    else {
	PARAMETER <- k
	names(NVAL) <- names(ESTIMATE)
    }
    names(PARAMETER) <- "df"

    x <- cbind(x, n - x)
    E <- cbind(n * p, n * (1 - p))
    if (any(E < 5))
	warning("Chi-squared approximation may be incorrect")
    STATISTIC <- sum((abs(x - E) - YATES)^2 / E)
    names(STATISTIC) <- "X-squared"

    if (alternative == "two.sided")
	PVAL <- pchisq(STATISTIC, PARAMETER, lower.tail = FALSE)
    else {
	if (k == 1)
	    z <- sign(ESTIMATE - p) * sqrt(STATISTIC)
	else
	    z <- sign(DELTA) * sqrt(STATISTIC)
	PVAL <- pnorm(z, lower.tail = (alternative == "less"))
    }

    RVAL <- list(statistic = STATISTIC,
		 parameter = PARAMETER,
		 p.value = as.numeric(PVAL),
		 estimate = ESTIMATE,
		 null.value = NVAL,
		 conf.int = CINT,
		 alternative = alternative,
		 method = METHOD,
		 data.name = DNAME)
    class(RVAL) <- "htest"
    return(RVAL)
}
