PMCMRplus (version 1.9.12)

medianAllPairsTest: Brown-Mood All Pairs Median Test

Description

Performs Brown-Mood All Pairs Median Test.

Usage

medianAllPairsTest(x, ...)
# S3 method for default
medianAllPairsTest(x, g, p.adjust.method = p.adjust.methods, ...)
# S3 method for formula
medianAllPairsTest(
  formula,
  data,
  subset,
  na.action,
  p.adjust.method = p.adjust.methods,
  ...
)

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.

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.

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 Brown-Mood non-parametric Median test can be performed. A total of \(m = k(k-1)/2\) hypotheses can be tested. The null hypothesis H\(_{ij}: \mu_i(x) = \mu_j(x)\) is tested in the two-tailed test against the alternative A\(_{ij}: \mu_i(x) \ne \mu_j(x), ~~ i \ne j\).

In this procedure the joined median is used for classification, but pairwise Pearson Chisquare-Tests are conducted. Any method as given by p.adjust.methods can be used to account for multiplicity.

References

Brown, G.W., Mood, A.M., 1951, On Median Tests for Linear Hypotheses, in: Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, pp. 159–167.

See Also

chisq.test.

Examples

## Data set InsectSprays
## Global test
kruskalTest(count ~ spray, data = InsectSprays)

## Conover's all-pairs comparison test
## single-step means Tukey's p-adjustment
ans <- kwAllPairsConoverTest(count ~ spray, data = InsectSprays,
                             p.adjust.method = "single-step")
summary(ans)

## Dunn's all-pairs comparison test
ans <- kwAllPairsDunnTest(count ~ spray, data = InsectSprays,
                             p.adjust.method = "bonferroni")
summary(ans)

## Nemenyi's all-pairs comparison test
ans <- kwAllPairsNemenyiTest(count ~ spray, data = InsectSprays)
summary(ans)

## Brown-Mood all-pairs median test
ans <- medianAllPairsTest(count ~ spray, data = InsectSprays)
summary(ans)