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Download Everything Offline Helpwilcox.test.R（R软件中的wilcox.test函数）
File src/library/stats/R/wilcox.test.R
Part of the R package, http://www.R-project.org
This prog you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software F 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.
GNU General Public License for more details.
A copy of the GNU General Public License is available at
http://www.r-project.org/Licenses/
wilcox.test &- function(x, ...) UseMethod("wilcox.test")
wilcox.test.default &-
function(x, y = NULL, alternative = c("two.sided", "less", "greater"),
mu = 0, paired = FALSE, exact = NULL, correct = TRUE,
conf.int = FALSE, conf.level = 0.95, ...)
alternative &- match.arg(alternative)
if(!missing(mu) && ((length(mu) & 1L) || !is.finite(mu)))
stop("'mu' must be a single number")
if(conf.int) {
if(!((length(conf.level) == 1L)
&& is.finite(conf.level)
&& (conf.level & 0)
&& (conf.level & 1)))
stop("'conf.level' must be a single number between 0 and 1")
if(!is.numeric(x)) stop("'x' must be numeric")
if(!is.null(y)) {
if(!is.numeric(y)) stop("'y' must be numeric")
DNAME &- paste(deparse(substitute(x)), "and",
deparse(substitute(y)))
if(paired) {
if(length(x) != length(y))
stop("'x' and 'y' must have the same length")
OK &- complete.cases(x, y)
x &- x[OK] - y[OK]
x &- x[is.finite(x)]
y &- y[is.finite(y)]
DNAME &- deparse(substitute(x))
if(paired)
stop("'y' is missing for paired test")
x &- x[is.finite(x)]
if(length(x) & 1L)
stop("not enough (finite) 'x' observations")
CORRECTION &- 0
if(is.null(y)) {
METHOD &- "Wilcoxon signed rank test"
x &- x - mu
ZEROES &- any(x == 0)
if(ZEROES)
x &- x[x != 0]
n &- as.double(length(x))
if(is.null(exact))
exact &- (n & 50)
r &- rank(abs(x))
STATISTIC &- sum(r[x & 0])
names(STATISTIC) &- "V"
TIES &- length(r) != length(unique(r))
if(exact && !TIES && !ZEROES) {
switch(alternative,
"two.sided" = {
p &- if(STATISTIC & (n * (n + 1) / 4))
psignrank(STATISTIC - 1, n, lower.tail = FALSE)
else psignrank(STATISTIC, n)
min(2 * p, 1)
"greater" = psignrank(STATISTIC - 1, n, lower.tail = FALSE),
"less" = psignrank(STATISTIC, n))
if(conf.int) {
## Exact confidence interval for the median in the
## one-sample case.
When used with paired values this
## gives a confidence interval for mean(x) - mean(y).
x &- x + mu
# we want a conf.int for the median
alpha &- 1 - conf.level
diffs &- outer(x, x, "+")
diffs &- sort(diffs[!lower.tri(diffs)]) / 2
switch(alternative,
"two.sided" = {
qu &- qsignrank(alpha / 2, n)
if(qu == 0) qu &- 1
ql &- n*(n+1)/2 - qu
achieved.alpha &- 2*psignrank(trunc(qu)-1,n)
c(diffs[qu], diffs[ql+1])
"greater"= {
qu &- qsignrank(alpha, n)
if(qu == 0) qu &- 1
achieved.alpha &- psignrank(trunc(qu)-1,n)
c(diffs[qu], +Inf)
qu &- qsignrank(alpha, n)
if(qu == 0) qu &- 1
ql &- n*(n+1)/2 - qu
achieved.alpha &- psignrank(trunc(qu)-1,n)
c(-Inf, diffs[ql+1])
if (achieved.alpha - alpha & alpha/2){
warning("Requested conf.level not achievable")
conf.level&- 1 - signif(achieved.alpha, 2)
attr(cint, "conf.level") &- conf.level
ESTIMATE &- median(diffs)
names(ESTIMATE) &- "(pseudo)median"
} else { ## not exact, maybe ties or zeroes
NTIES &- table(r)
z &- STATISTIC - n * (n + 1)/4
SIGMA &- sqrt(n * (n + 1) * (2 * n + 1) / 24
- sum(NTIES^3 - NTIES) / 48)
if(correct) {
CORRECTION &-
switch(alternative,
"two.sided" = sign(z) * 0.5,
"greater" = 0.5,
"less" = -0.5)
METHOD &- paste(METHOD, "with continuity correction")
z &- (z - CORRECTION) / SIGMA
PVAL &- switch(alternative,
"less" = pnorm(z),
"greater" = pnorm(z, lower.tail=FALSE),
"two.sided" = 2 * min(pnorm(z),
pnorm(z, lower.tail=FALSE)))
if(conf.int) {
## Asymptotic confidence interval for the median in the
## one-sample case.
When used with paired values this
## gives a confidence interval for mean(x) - mean(y).
## Algorithm not published, thus better documented here.
x &- x + mu
alpha &- 1 - conf.level
## These are sample based limits for the median
## [They don't work if alpha is too high]
mumin &- min(x)
mumax &- max(x)
## wdiff(d, zq) returns the absolute difference between
## the asymptotic Wilcoxon statistic of x - mu - d and
## the quantile zq.
wdiff &- function(d, zq) {
xd &- x - d
xd &- xd[xd != 0]
nx &- length(xd)
dr &- rank(abs(xd))
zd &- sum(dr[xd & 0]) - nx * (nx + 1)/4
NTIES.CI &- table(dr)
SIGMA.CI &- sqrt(nx * (nx + 1) * (2 * nx + 1) / 24
- sum(NTIES.CI^3 - NTIES.CI) / 48)
if (SIGMA.CI == 0)
stop("cannot compute confidence interval when all observations are tied", call.=FALSE)
CORRECTION.CI &-
if(correct) {
switch(alternative,
"two.sided" = sign(zd) * 0.5,
"greater" = 0.5,
"less" = -0.5)
(zd - CORRECTION.CI) / SIGMA.CI - zq
## Here we optimize the function wdiff in d over the set
## c(mumin, mumax).
## This returns a value from c(mumin, mumax) for which
## the asymptotic Wilcoxon statistic is equal to the
## quantile zq.
This means that the statistic is not
## within the critical region, and that implies that d
## is a confidence limit for the median.
## As in the exact case, interchange quantiles.
cint &- switch(alternative, "two.sided" = {
mindiff &- wdiff(mumin,zq = qnorm(alpha/2, lower.tail = FALSE))
maxdiff &- wdiff(mumax,zq = qnorm(alpha/2))
if(mindiff & 0 || maxdiff & 0)
alpha &- alpha*2
else break
if(1 - conf.level & alpha*0.75) {
conf.level &- 1 - alpha
warning("Requested conf.level not achievable")
l &- uniroot(wdiff, c(mumin, mumax), tol=1e-4,
zq=qnorm(alpha/2, lower.tail=FALSE))$root
u &- uniroot(wdiff, c(mumin, mumax), tol=1e-4,
zq = qnorm(alpha/2))$root
}, "greater" = {
mindiff &- wdiff(mumin, zq = qnorm(alpha, lower.tail = FALSE))
if(mindiff & 0)
alpha &- alpha*2
else break
if(1 - conf.level & alpha*0.75) {
conf.level &- 1 - alpha
warning("Requested conf.level not achievable")
l &- uniroot(wdiff, c(mumin, mumax), tol = 1e-4,
zq = qnorm(alpha, lower.tail = FALSE))$root
c(l, +Inf)
}, "less" = {
maxdiff &- wdiff(mumax, zq = qnorm(alpha))
if(maxdiff & 0)
alpha &- alpha * 2
else break
if (1 - conf.level & alpha*0.75) {
conf.level &- 1 - alpha
warning("Requested conf.level not achievable")
u &- uniroot(wdiff, c(mumin, mumax), tol=1e-4,
zq = qnorm(alpha))$root
c(-Inf, u)
attr(cint, "conf.level") &- conf.level
correct &- FALSE # no continuity correction for estimate
ESTIMATE &- uniroot(wdiff, c(mumin, mumax), tol=1e-4,
zq = 0)$root
names(ESTIMATE) &- "(pseudo)median"
if(exact && TIES) {
warning("cannot compute exact p-value with ties")
if(conf.int)
warning("cannot compute exact confidence interval with ties")
if(exact && ZEROES) {
warning("cannot compute exact p-value with zeroes")
if(conf.int)
warning("cannot compute exact confidence interval with zeroes")
else { ##-------------------------- 2-sample case ---------------------------
if(length(y) & 1L)
stop("not enough 'y' observations")
METHOD &- "Wilcoxon rank sum test"
r &- rank(c(x - mu, y))
n.x &- as.double(length(x))
n.y &- as.double(length(y))
if(is.null(exact))
exact &- (n.x & 50) && (n.y & 50)
STATISTIC &- sum(r[seq_along(x)]) - n.x * (n.x + 1) / 2
names(STATISTIC) &- "W"
TIES &- (length(r) != length(unique(r)))
if(exact && !TIES) {
switch(alternative,
"two.sided" = {
p &- if(STATISTIC & (n.x * n.y / 2))
pwilcox(STATISTIC - 1, n.x, n.y, lower.tail = FALSE)
pwilcox(STATISTIC, n.x, n.y)
min(2 * p, 1)
"greater" = {
pwilcox(STATISTIC - 1, n.x, n.y, lower.tail = FALSE)
"less" = pwilcox(STATISTIC, n.x, n.y))
if(conf.int) {
## Exact confidence interval for the location parameter
## mean(x) - mean(y) in the two-sample case (cf. the
## one-sample case).
alpha &- 1 - conf.level
diffs &- sort(outer(x, y, "-"))
switch(alternative,
"two.sided" = {
qu &- qwilcox(alpha/2, n.x, n.y)
if(qu == 0) qu &- 1
ql &- n.x*n.y - qu
achieved.alpha &- 2*pwilcox(trunc(qu)-1,n.x,n.y)
c(diffs[qu], diffs[ql + 1])
"greater"= {
qu &- qwilcox(alpha, n.x, n.y)
if(qu == 0) qu &- 1
achieved.alpha &- pwilcox(trunc(qu)-1,n.x,n.y)
c(diffs[qu], +Inf)
qu &- qwilcox(alpha, n.x, n.y)
if(qu == 0) qu &- 1
ql &- n.x*n.y - qu
achieved.alpha &- pwilcox(trunc(qu)-1,n.x,n.y)
c(-Inf, diffs[ql + 1])
if (achieved.alpha-alpha & alpha/2) {
warning("Requested conf.level not achievable")
conf.level &- 1 - achieved.alpha
attr(cint, "conf.level") &- conf.level
ESTIMATE &- median(diffs)
names(ESTIMATE) &- "difference in location"
NTIES &- table(r)
z &- STATISTIC - n.x * n.y / 2
SIGMA &- sqrt((n.x * n.y / 12) *
((n.x + n.y + 1)
- sum(NTIES^3 - NTIES)
/ ((n.x + n.y) * (n.x + n.y - 1))))
if(correct) {
CORRECTION &- switch(alternative,
"two.sided" = sign(z) * 0.5,
"greater" = 0.5,
"less" = -0.5)
METHOD &- paste(METHOD, "with continuity correction")
z &- (z - CORRECTION) / SIGMA
PVAL &- switch(alternative,
"less" = pnorm(z),
"greater" = pnorm(z, lower.tail=FALSE),
"two.sided" = 2 * min(pnorm(z),
pnorm(z, lower.tail=FALSE)))
if(conf.int) {
## Asymptotic confidence interval for the location
## parameter mean(x) - mean(y) in the two-sample case
## (cf. one-sample case).
## Algorithm not published, for a documentation see the
## one-sample case.
alpha &- 1 - conf.level
mumin &- min(x) - max(y)
mumax &- max(x) - min(y)
wdiff &- function(d, zq) {
dr &- rank(c(x - d, y))
NTIES.CI &- table(dr)
dz &- (sum(dr[seq_along(x)])
- n.x * (n.x + 1) / 2 - n.x * n.y / 2)
CORRECTION.CI &-
if(correct) {
switch(alternative,
"two.sided" = sign(dz) * 0.5,
"greater" = 0.5,
"less" = -0.5)
SIGMA.CI &- sqrt((n.x * n.y / 12) *
((n.x + n.y + 1)
- sum(NTIES.CI^3 - NTIES.CI)
/ ((n.x + n.y) * (n.x + n.y - 1))))
if (SIGMA.CI == 0)
stop("cannot compute confidence interval when all observations are tied", call.=FALSE)
(dz - CORRECTION.CI) / SIGMA.CI - zq
root &- function(zq) {
## in extreme cases we need to return endpoints,
wilcox.test(1, 2:60, conf.int=TRUE)
f.lower &- wdiff(mumin, zq)
if(f.lower &= 0) return(mumin)
f.upper &- wdiff(mumax, zq)
if(f.upper &= 0) return(mumax)
uniroot(wdiff, c(mumin, mumax),
f.lower = f.lower, f.upper = f.upper,
tol = 1e-4, zq = zq)$root
cint &- switch(alternative, "two.sided" = {
l &- root(zq=qnorm(alpha/2, lower.tail=FALSE))
u &- root(zq=qnorm(alpha/2))
}, "greater"= {
l &- root(zq=qnorm(alpha, lower.tail=FALSE))
c(l, +Inf)
}, "less"= {
u &- root(zq=qnorm(alpha))
c(-Inf, u)
attr(cint, "conf.level") &- conf.level
correct &- FALSE # no continuity correction for estimate
ESTIMATE &- uniroot(wdiff, c(mumin, mumax), tol=1e-4,
zq=0)$root
names(ESTIMATE) &- "difference in location"
if(exact && TIES) {
warning("cannot compute exact p-value with ties")
if(conf.int)
warning("cannot compute exact confidence intervals with ties")
names(mu) &- if(paired || !is.null(y)) "location shift" else "location"
RVAL &- list(statistic = STATISTIC,
parameter = NULL,
p.value = as.numeric(PVAL),
null.value = mu,
alternative = alternative,
method = METHOD,
data.name = DNAME)
if(conf.int)
RVAL &- c(RVAL,
list(conf.int = cint,
estimate = ESTIMATE))
class(RVAL) &- "htest"
return(RVAL)
wilcox.test.formula &-
function(formula, data, subset, na.action, ...)
if(missing(formula)
|| (length(formula) != 3L)
|| (length(attr(terms(formula[-2L]), "term.labels")) != 1L))
stop("'formula' missing or incorrect")
m &- match.call(expand.dots = FALSE)
if(is.matrix(eval_r(m$data, parent.frame())))
m$data &- as.data.frame(data)
m[[1L]] &- as.name("model.frame")
m$... &- NULL
mf &- eval_r(m, parent.frame())
DNAME &- paste(names(mf), collapse = " by ")
names(mf) &- NULL
response &- attr(attr(mf, "terms"), "response")
g &- factor(mf[[-response]])
if(nlevels(g) != 2L)
stop("grouping factor must have exactly 2 levels")
DATA &- split(mf[[response]], g)
names(DATA) &- c("x", "y")
y &- do.call("wilcox.test", c(DATA, list(...)))
y$data.name &- DNAME
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