kwAllPairsDunnTest {PMCMRplus}

Dunn's All-Pairs Rank Comparison Test

Description

Performs Dunn's non-parametric all-pairs comparison test for Kruskal-type ranked data.

Usage

kwAllPairsDunnTest(x, ...)

## Default S3 method:
kwAllPairsDunnTest(x, g, p.adjust.method = p.adjust.methods, ...)

## S3 method for class 'formula'
kwAllPairsDunnTest(
  formula,
  data,
  subset,
  na.action,
  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.

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 Dunn's non-parametric 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.

The p-values are computed from the standard normal distribution using any of the p-adjustment methods as included in p.adjust. Originally, Dunn (1964) proposed Bonferroni's p-adjustment method.

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

Dunn, O. J. (1964) Multiple comparisons using rank sums, Technometrics 6, 241–252.

Siegel, S., Castellan Jr., N. J. (1988) Nonparametric Statistics for The Behavioral Sciences. New York: McGraw-Hill.

See Also

Normal, p.adjust, kruskalTest, kwAllPairsConoverTest, kwAllPairsNemenyiTest

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)