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

In PMCMRplus: Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

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

Description

Performs Murakami's modified Baumgartner-Weiß-Schindler test for testing against ordered alternatives.

Usage

bwsTrendTest(x, ...)

## Default S3 method:
bwsTrendTest(x, g, nperm = 1000, ...)

## S3 method for class '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").

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.

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.

Note

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.

Factor labels for g must be assigned in such a way, that they can be increasingly ordered from zero-dose control to the highest dose level, e.g. integers {0, 1, 2, ..., k} or letters {a, b, c, ...}. Otherwise the function may not select the correct values for intended zero-dose control.

It is safer, to i) label the factor levels as given above, and to ii) sort the data according to increasing dose-levels prior to call the function (see order, factor).

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.

Neuhäuser, M. (2001) One-Side Two-Sample and Trend Tests Based on a Modified Baumgartner-Weiss-Schindler Statistic. J Nonparametric Stat 13, 729–739.

See Also

sample, bwsAllPairsTest, bwsManyOneTest.

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

Examples

## 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)

PMCMRplus documentation built on Nov. 27, 2023, 1:08 a.m.