wilcox.test {ctest}R Documentation

Wilcoxon Rank Sum and Signed Rank Tests

Description

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

Usage

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

Arguments

x numeric vector of data values.
y 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.
mu 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.

Details

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.

Value

A list with class "htest" containing the following components:
statistic the value of the test statistic with a name describing it.
parameter the parameter(s) for the exact distribution of the test statistic.
p.value the p-value for the test.
null.value the location parameter mu.
alternative a character string describing the alternative hypothesis.
method the type of test applied.
data.name a character string giving the names of the data.

References

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

See Also

kruskal.test for testing homogeneity in location parameters in the case of two or more samples; t.test for a parametric alternative under normality assumptions.

Examples

## 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.test(x, y, paired = TRUE, alternative = "greater")
wilcox.test(y - x, alternative = "less")    # The same.
wilcox.test(y - x, alternative = "less",
            exact = FALSE, correct = FALSE) # H&W large sample
                                            # approximation

## 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.test(x, y, alternative = "g")# greater
wilcox.test(x, y, alternative = "greater",
            exact = FALSE, correct = FALSE) # H&W large sample
                                            # approximation

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