Murakami's k-Sample BWS Test
Performs Murakami's k-Sample BWS Test.
bwsKSampleTest(x, ...) ## Default S3 method: bwsKSampleTest(x, g, nperm = 1000, ...) ## S3 method for class 'formula' bwsKSampleTest(formula, data, subset, na.action, nperm = 1000, ...)
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 |
nperm |
number of permutations for the assymptotic permutation test.
Defaults 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 |
Let X_{ij} ~ (1 ≤ i ≤ k,~ 1 ≤ 1 ≤ n_i) denote an identically and independently distributed variable that is obtained from an unknown continuous distribution F_i(x). Let R_{ij} be the rank of X_{ij}, where X_{ij} is jointly ranked from 1 to N, ~ N = ∑_{i=1}^k n_i. In the k-sample test the null hypothesis, H: F_i = F_j is tested against the alternative, A: F_i \ne F_j ~~(i \ne j) with at least one inequality beeing strict. Murakami (2006) has generalized the two-sample Baumgartner-Weiß-Schindler test (Baumgartner et al. 1998) and proposed a modified statistic B_k^* defined by
SEE PDF
where
SEE PDF
and
SEE PDF
The p-values are estimated via an assymptotic boot-strap method. It should be noted that the B_k^* detects both differences in the unknown location parameters and / or differences in the unknown scale parameters of the k-samples.
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.
One may increase the number of permutations to e.g. nperm = 10000
in order to get more precise p-values. However, this will be on
the expense of computational time.
Baumgartner, W., Weiss, P., Schindler, H. (1998) A nonparametric test for the general two-sample problem, Biometrics 54, 1129–1135.
Murakami, H. (2006) K-sample rank test based on modified Baumgartner statistic and its power comparison, J. Jpn. Comp. Statist. 19, 1–13.
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.