bwsAllPairsTest {PMCMRplus}

BWS All-Pairs Comparison Test

Description

Performs Baumgartner-Weiß-Schindler all-pairs comparison test.

Usage

bwsAllPairsTest(x, ...)

## Default S3 method:
bwsAllPairsTest(
  x,
  g,
  method = c("BWS", "Murakami"),
  p.adjust.method = p.adjust.methods,
  ...
)

## S3 method for class 'formula'
bwsAllPairsTest(
  formula,
  data,
  subset,
  na.action,
  method = c("BWS", "Murakami"),
  p.adjust.method = p.adjust.methods,
  ...
)

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.

method

a character string specifying the test statistic to use. Defaults to BWS.

p.adjust.method

method for adjusting p values (see p.adjust).

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

For all-pairs comparisons in an one-factorial layout with non-normally distributed residuals Baumgartner-Weiß-Schindler all-pairs comparison test can be used. A total of m = k(k-1)/2 hypotheses can be tested. The null hypothesis H_{ij}: F_i(x) = F_j(x) is tested in the two-tailed test against the alternative A_{ij}: F_i(x) \ne F_j(x), ~~ i \ne j.

This function is a wrapper function that sequentially calls bws_test for each pair. The default test method ("BWS") is the original Baumgartner-Weiß-Schindler test statistic B. For method == "Murakami" it is the modified BWS statistic denoted B*. The calculated p-values for Pr(>|B|) or Pr(>|B*|) can be adjusted to account for Type I error inflation using any method as implemented in p.adjust.

Value

A list with class "PMCMR" 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

lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

lower-triangle matrix of the p-values for the pairwise tests.

alternative

a character string describing the alternative hypothesis.

p.adjust.method

a character string describing the method for p-value adjustment.

model

a data frame of the input data.

dist

a string that denotes the test distribution.

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.

See Also

bws_test.

Examples

out <- bwsAllPairsTest(count ~ spray, InsectSprays, p.adjust="holm")
summary(out)
summaryGroup(out)