wilcox.test {ctest} | R Documentation |

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

wilcox.test(x, ...) ## Default S3 method: wilcox.test(x, y = NULL, alternative = c("two.sided", "less", "greater"), mu = 0, paired = FALSE, exact = NULL, correct = TRUE, conf.int = FALSE, conf.level = 0.95, ...) ## S3 method for class 'formula': wilcox.test(formula, data, subset, na.action, ...)

`x` |
numeric vector of data values. |

`y` |
an optional numeric vector of data values. |

`alternative` |
a character string specifying 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. |

`conf.int` |
a logical indicating whether a confidence interval should be computed. |

`conf.level` |
confidence level of the interval. |

`formula` |
a formula of the form `lhs ~ rhs` where `lhs`
is a numeric variable giving the data values and `rhs` a factor
with two levels giving the corresponding groups. |

`data` |
an optional data frame containing the variables in the model formula. |

`subset` |
an optional vector specifying a subset of observations to be used. |

`na.action` |
a function which indicates what should happen when
the data contain `NA` s. Defaults to
`getOption("na.action")` . |

`...` |
further arguments to be passed to or from methods. |

The formula interface is only applicable for the 2-sample tests.

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 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`

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 and an estimator for the pseudomedian (one-sample
case) or for the difference of the location parameters `x-y`

is
computed. (The pseudomedian of a distribution *F* is the median
of the distribution of *(u+v)/2*, where *u* and *v* are
independent, each with distribution *F*. If *F* is symmetric,
then the pseudomedian and median coincide. See Hollander & Wolfe
(1973), page 34.) If exact p-values are available, an exact
confidence interval is obtained by the algorithm described in Bauer
(1972), and the Hodges-Lehmann estimator is employed. Otherwise, the
returned confidence interval and point estimate are based on normal
approximations.

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. |

`conf.int` |
a confidence interval for the location parameter.
(Only present if argument `conf.int = TRUE` .) |

`estimate` |
an estimate of the location parameter.
(Only present if argument `conf.int = TRUE` .) |

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.

`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.

## 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 wilcox.test(rnorm(10), rnorm(10, 2), conf.int = TRUE) ## Formula interface. data(airquality) boxplot(Ozone ~ Month, data = airquality) wilcox.test(Ozone ~ Month, data = airquality, subset = Month %in% c(5, 8))