kruskalTest {PMCMRplus} | R Documentation |
Performs a Kruskal-Wallis rank sum test.
kruskalTest(x, ...) ## Default S3 method: kruskalTest(x, g, dist = c("Chisquare", "KruskalWallis", "FDist"), ...) ## S3 method for class 'formula' kruskalTest( formula, data, subset, na.action, dist = c("Chisquare", "KruskalWallis", "FDist"), ... )
x |
a numeric vector of data values, or a list of numeric data vectors. |
... |
further arguments to be passed to or from methods. |
g |
a vector or factor object giving the group for the
corresponding elements of |
dist |
the test distribution. Defaults's to |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
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 |
For one-factorial designs with non-normally distributed residuals the Kruskal-Wallis rank sum test can be performed to test the H_0: F_1(x) = F_2(x) = … = F_k(x) against the H_\mathrm{A}: F_i (x) \ne F_j(x)~ (i \ne j) with at least one strict inequality.
As the Kruskal-Wallis H-statistic is assymptotically
chi-squared distributed with v = k - 1 degree
of freedom, the default test distribution is consequently
dist = "Chisquare"
. If dist = "KruskalWallis"
is selected,
an incomplete beta approximation is used for the calculation
of p-values as implemented in the function
pKruskalWallis
of the package
SuppDists. For dist = "FDist"
the proposed method of Conover and Imam (1981) is used, which is
equivalent to a one-way ANOVA F-test using rank transformed data
(see examples).
A list with class "htest"
containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated quantile of the test statistic.
the p-value for the test.
the parameters of the test statistic, if any.
a character string describing the alternative hypothesis.
the estimates, if any.
the estimate under the null hypothesis, if any.
Conover, W. J., Iman, R. L. (1981) Rank transformations as a bridge between parametric and nonparametric statistics, The American Statistician 35, 124–129.
Sachs, L. (1997) Angewandte Statistik. Berlin: Springer.
kruskal.test
, pKruskalWallis
,
Chisquare
, FDist
## Hollander & Wolfe (1973), 116. ## Mucociliary efficiency from the rate of removal of dust in normal ## subjects, subjects with obstructive airway disease, and subjects ## with asbestosis. x <- c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects y <- c(3.8, 2.7, 4.0, 2.4) # with obstructive airway disease z <- c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis g <- factor(x = c(rep(1, length(x)), rep(2, length(y)), rep(3, length(z))), labels = c("ns", "oad", "a")) dat <- data.frame( g = g, x = c(x, y, z)) ## AD-Test adKSampleTest(x ~ g, data = dat) ## BWS-Test bwsKSampleTest(x ~ g, data = dat) ## Kruskal-Test ## Using incomplete beta approximation kruskalTest(x ~ g, dat, dist="KruskalWallis") ## Using chisquare distribution kruskalTest(x ~ g, dat, dist="Chisquare") ## Not run: ## Check with kruskal.test from R stats kruskal.test(x ~ g, dat) ## End(Not run) ## Using Conover's F kruskalTest(x ~ g, dat, dist="FDist") ## Not run: ## Check with aov on ranks anova(aov(rank(x) ~ g, dat)) ## Check with oneway.test oneway.test(rank(x) ~ g, dat, var.equal = TRUE) ## End(Not run)