PMCMRplus (version 1.9.3)

kwAllPairsDunnTest: 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, ...)
# S3 method for default
kwAllPairsDunnTest(x, g, p.adjust.method = p.adjust.methods, ...)
# S3 method for 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").

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.

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.

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

# NOT RUN {
## 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)
# }