PMCMRplus (version 1.9.3)

bwsTrendTest: Testing against Ordered Alternatives (Murakami's BWS Trend Test)

Description

Performs Murakami's modified Baumgartner-Wei<U+00DF>-Schindler test for testing against ordered alternatives.

Usage

bwsTrendTest(x, ...)
# S3 method for default
bwsTrendTest(x, g, nperm = 1000, ...)
# S3 method for formula
bwsTrendTest(formula, data, subset, na.action, nperm = 1000, ...)

Arguments

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 "x". Ignored with a warning if "x" is a list.

nperm

number of permutations for the assymptotic permutation test. Defaults to 1000.

formula

a formula of the form response ~ group where response gives the data values and group a vector or factor of the corresponding groups.

data

an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(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 NAs. Defaults to getOption("na.action").

Value

A list with class "htest" containing the following components:

method

a character string indicating what type of test was performed.

data.name

a character string giving the name(s) of the data.

statistic

the estimated quantile of the test statistic.

p.value

the p-value for the test.

parameter

the parameters of the test statistic, if any.

alternative

a character string describing the alternative hypothesis.

estimates

the estimates, if any.

null.value

the estimate under the null hypothesis, if any.

Details

The null hypothesis, H\(_0: F_1(u) = F_2(u) = \ldots = F_k(u) ~~ u \in R\) is tested against a simple order hypothesis, H\(_\mathrm{A}: F_1(u) \le F_2(u) \le \ldots \le F_k(u),~F_1(u) < F_k(u), ~~ u \in R\).

The p-values are estimated through an assymptotic boot-strap method using the function sample.

References

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.

Neuh<U+00E4>user, M. (2001) One-side two-sample and trend tests based on a modified Baumgartner-Weiss-Schindler statistic. Journal of Nonparametric Statistics 13, 729--739.

See Also

sample, bwsAllPairsTest, bwsManyOneTest.

kruskalTest and shirleyWilliamsTest of the package PMCMRplus, kruskal.test of the library stats.

Examples

# NOT RUN {
## Example from Sachs (1997, p. 402)
x <- c(106, 114, 116, 127, 145,
       110, 125, 143, 148, 151,
       136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")

## Chacko's test
chackoTest(x, g)

## Cuzick's test
cuzickTest(x, g)

## Johnson-Mehrotra test
johnsonTest(x, g)

## Jonckheere-Terpstra test
jonckheereTest(x, g)

## Le's test
leTest(x, g)

## Spearman type test
spearmanTest(x, g)

## Murakami's BWS trend test
bwsTrendTest(x, g)

## Fligner-Wolfe test
flignerWolfeTest(x, g)

## Shan-Young-Kang test
shanTest(x, g)

# }