View source: R/bwsKSampleTest.R
bwsKSampleTest | R Documentation |
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 \le i \le k,~ 1 \le 1 \le 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 = \sum_{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
B_{k}^* = \frac{1}{k}\sum_{i=1}^k
\left\{\frac{1}{n_i} \sum_{j=1}^{n_i} \frac{(R_{ij} - \mathsf{E}[R_{ij}])^2}
{\mathsf{Var}[R_{ij}]}\right\},
where
\mathsf{E}[R_{ij}] = \frac{N + 1}{n_i + 1} j
and
\mathsf{Var}[R_{ij}] = \frac{j}{n_i + 1} \left(1 - \frac{j}{n_i + 1}\right)
\frac{\left(N-n_i\right)\left(N+1\right)}{n_i + 2}.
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.
sample
, bwsAllPairsTest
,
bwsManyOneTest
.
## 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)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.