Wilcoxon Exact Test

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

wilcoxe.test(
  x,
  y = NULL,
  mu = 0,
  paired = FALSE,
  alternative = c("two.sided", "less", "greater"),
  conf.level = 0.95
)

Arguments

x: is a numeric vector of data values. Non-finite (i.e. infinite or missing) values will be omitted.
y: an optional numeric vector of data values
mu: a number specifying an optional parameter used to form the null hypothesis
paired: a logical indicating whether you want a paired test
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "less", or "greater". You can specify just the initial letter.
conf.level: confidence level of the interval

Value

A list of class htest, containing the following components:

statistic: the value of the test statistic with a name describing it
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
conf.int: a confidence interval for the location parameter
estimate: an estimate of the location parameter

Details

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

Otherwise, if both x and y are given and paired = FALSE, a Wilcoxon rank sum test is done. In this case, the null hypothesis is that the distribution of x and y differ by a location shift mu, and the alternative is that they differ by some other location shift (and the one-sided alternative "greater" is that x is shifted to the right of y).

Note

The function is rather primitive and should only be used for problems with fewer than 19 observations as the memory requirements are rather large.

References

Gibbons, J.D. and Chakraborti, S. 1992. Nonparametric Statistical Inference. Marcel Dekker Inc., New York.
Hollander, M. and Wolfe, D.A. 1999. Nonparametric Statistical Methods. New York: John Wiley & Sons.

Author

Alan T. Arnholt <arnholtat@appstate.edu>

Examples

 
# Wilcoxon Signed Rank Test
PH <- c(7.2, 7.3, 7.3, 7.4)
wilcoxe.test(PH, mu = 7.25, alternative = "greater")
#> 
#> 	Wilcoxon Signed Rank Test
#> 
#> data:  PH
#> t+ = 8, p-value = 0.25
#> alternative hypothesis: true median is greater than 7.25
#> 93.75 percent confidence interval:
#>  7.25  Inf
#> sample estimates:
#> (pseudo)median 
#>            7.3 
#> 
# Wilcoxon Signed Rank Test (Dependent Samples)
with(data = AGGRESSION, 
wilcoxe.test(violence, noviolence, paired = TRUE, alternative = "greater"))
#> 
#> 	Wilcoxon Signed Rank Test (Dependent Samples)
#> 
#> data:  violence and noviolence
#> t+ = 118.5, p-value = 0.003265
#> alternative hypothesis: true median difference is greater than 0
#> 95.20569 percent confidence interval:
#>    2 Inf
#> sample estimates:
#> (pseudo)median 
#>            4.5 
#> 
# Wilcoxon Rank Sum Test
x <- c(7.2, 7.2, 7.3, 7.3)
y <- c(7.3, 7.3, 7.4, 7.4)
wilcoxe.test(x, y)
#> 
#> 	Wilcoxon Rank Sum Test
#> 
#> data:  x and y
#> w = 12, p-value = 0.1714
#> alternative hypothesis: true median is not equal to 0
#> 82.85714 percent confidence interval:
#>  -0.2  0.0
#> sample estimates:
#> difference in location 
#>                   -0.1 
#> 
rm(PH, x, y)