wilcox.exact: Wilcoxon Rank Sum and Signed Rank Tests

Description

Performs one and two sample Wilcoxon tests on vectors of data. Version for exactRankTests.

Usage

wilcox.exact(x, y = NULL, alternative = c("two.sided", "less", "greater"),
            mu = 0, paired = FALSE, exact = NULL, correct = TRUE, 
            conf.int = FALSE, conf.level = 0.95)

Arguments

numeric vector of data values.

an optional numeric vector of data values.

alternative

the alternative hypothesis must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

a number specifying an optional location parameter.

paired

a logical indicating whether you want a paired test.

exact

a logical indicating whether an exact p-value should be computed.

correct

a logical indicating whether to apply continuity correction in the normal approximation for the p-value.

conf.int

a logical indicating whether a confidence interval should be computed.

conf.level

confidence level of the interval.

Value

A list with class "htest" containing the following components:
statisticthe value of the test statistic with a name describing it.
parameterthis gives the probability of observing the test statistic itself (named as point-prob). Useful for mid-p-values.
p.valuethe p-value for the test.
null.valuethe location parameter mu.
alternativea character string describing the alternative hypothesis.
methodthe type of test applied.
data.namea character string giving the names of the data.
conf.inta confidence interval for the location parameter. (Only present if argument conf.int = TRUE.)

Details

For testing proposes, this version computes p-values and quantiles using the Streitberg-R"ohmel algorithm (both for tied and untied samples).

If only x is given, or if both x and y are given and paired is TRUE, a Wilcoxon signed rank test of the null that the median of x (in the one sample case) or of x-y (in the paired two sample case) equals mu is performed.

Otherwise, if both x and y are given and paired is FALSE, a Wilcoxon rank sum test (equivalent to the Mann-Whitney test) is carried out. In this case, the null hypothesis is that the location of the distributions of x and y differ by mu.

By default (if exact is not specified), an exact p-value is computed if the samples contain less than 50 finite values and there are no ties. Otherwise, a normal approximation is used.

Optionally (if argument conf.int is true), a nonparametric confidence interval for the median (one-sample case) or for the difference of the location parameters x-y is computed. If exact p-values are available, an exact confidence interval is obtained by the algorithm described in Bauer (1972). Otherwise, an asymptotic confidence interval is returned.

References

Myles Hollander & Douglas A. Wolfe (1973), Nonparametric statistical inference. New York: John Wiley & Sons. Pages 27--33 (one-sample), 68--75 (two-sample).

David F. Bauer (1972), Constructing confidence sets using rank statistics. Journal of the American Statistical Association 67, 687--690.

Examples

Run this code

## One-sample test.
## Hollander & Wolfe (1973), 29f.
## Hamilton depression scale factor measurements in 9 patients with
##  mixed anxiety and depression, taken at the first (x) and second
##  (y) visit after initiation of a therapy (administration of a
##  tranquilizer).
x <- c(1.83,  0.50,  1.62,  2.48, 1.68, 1.88, 1.55, 3.06, 1.30)
y <- c(0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29)
wilcox.exact(x, y, paired = TRUE, alternative = "greater")
wilcox.exact(y - x, alternative = "less")    # The same.

stopifnot(wilcox.test(y-x)$p.value == wilcox.exact(y -x)$p.value)

## Two-sample test.
## Hollander & Wolfe (1973), 69f.
## Permeability constants of the human chorioamnion (a placental
##  membrane) at term (x) and between 12 to 26 weeks gestational
##  age (y).  The alternative of interest is greater permeability
##  of the human chorioamnion for the term pregnancy.
x <- c(0.80, 0.83, 1.89, 1.04, 1.45, 1.38, 1.91, 1.64, 0.73, 1.46)
y <- c(1.15, 0.88, 0.90, 0.74, 1.21)
wilcox.exact(x, y, alternative = "g")        # greater

x <- rnorm(10)
y <- rnorm(10, 2)
wilcox.exact(x, y, conf.int = TRUE)

<testonly>if (!any(duplicated(c(x,y)))) {
    we <- wilcox.exact(x, y, conf.int = TRUE)
    wt <- wilcox.test(x, y, conf.int = TRUE)
    we$parameter <- NULL
    we$method <- NULL
    wt$parameter <- NULL
    wt$method <- NULL
    stopifnot(all.equal(wt, we))
  }</testonly>
  

# Data from the StatXact-4 manual, page 221, diastolic blood pressure

treat <- c(94, 108, 110, 90)
contr <- c(80, 94, 85, 90, 90, 90, 108, 94, 78, 105, 88)

# StatXact 4 for Windows: p.value = 0.0989, point prob = 0.019

wilcox.exact(contr, treat, conf.int=T)

<testonly>we <- wilcox.exact(contr, treat, conf.int=T)
  stopifnot(we$estimate > we$conf.int[1] & we$estimate < we$conf.int[2])</testonly> 

# StatXact 4 for Windows: p.value = 0.0542, point prob = 0.019
 
wilcox.exact(contr, treat, alternative="less", conf.int=T) 

# paired observations
# Data from the StatXact-4 manual, page 167, serum antigen level

# StatXact 4 for Windows: p.value=0.0021 (page 168)

pre <- c(149, 0, 0, 259, 106, 255, 0, 52, 340, 65, 180, 0, 84, 89, 212, 554,
500, 424, 112, 2600)
post <- c(0, 51, 0, 385, 0, 235, 0, 0, 48, 65, 77, 0, 0, 0, 53, 150, 0, 165,
98, 0)

wilcox.exact(pre, post, paired=T, conf.int=T)

<testonly>we <- wilcox.exact(pre, post, paired=T, conf.int=T)
  stopifnot(we$estimate > we$conf.int[1] & we$estimate < we$conf.int[2])</testonly>

<testonly>stopifnot(wilcox.exact(1:8)$p.value == 0.0078125)
stopifnot(wilcox.exact(c(1:7,7))$p.value == 0.0078125)
stopifnot(wilcox.exact(c(1,1,1))$p.value == 0.25)

x <- rnorm(10)
y <- rnorm(10)
stopifnot(wilcox.test(x,y,conf.int=T)$estimate ==
          wilcox.exact(x,y,conf.int=T)$estimate)
stopifnot(wilcox.test(x,conf.int=T)$estimate ==
          wilcox.exact(x,conf.int=T)$estimate)</testonly>

Run the code above in your browser using DataLab