bwsAllPairsTest() R function from [PMCMRplus]

BWS All-Pairs Comparison Test

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


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").

Returns

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.

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.

Examples


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

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.

bwsAllPairsTest function