adAllPairsTest {PMCMRplus}

Anderson-Darling All-Pairs Comparison Test

Description

Performs Anderson-Darling all-pairs comparison test.

Usage

adAllPairsTest(x, ...)

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

## S3 method for class 'formula'
adAllPairsTest(
  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 Anderson-Darling's 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 adKSampleTest for each pair. The calculated p-values for Pr(>|T2N|) can be adjusted to account for Type I error multiplicity 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

Scholz, F.W., Stephens, M.A. (1987) K-Sample Anderson-Darling Tests. Journal of the American Statistical Association 82, 918–924.

See Also

adKSampleTest, adManyOneTest, ad.pval.

Examples

adKSampleTest(count ~ spray, InsectSprays)

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