R: All-Pairs Comparisons for Simply Ordered Mean Ranksums

chaAllPairsNashimotoTest {PMCMRplus}

R Documentation

All-Pairs Comparisons for Simply Ordered Mean Ranksums

Description

Performs Nashimoto and Wright's all-pairs comparison procedure for simply ordered mean ranksums (NPY' test and NPT' test). According to the authors, bove procedures shall only be applied after Chacko's test (see chackoTest) indicates global significance.

The modified procedure uses the property of a simple order, θ_m' - θ_m ≤ θ_j - θ_i ≤ θ_l' - θ_l \qquad (l ≤ i ≤ m~\mathrm{and}~ m' ≤ j ≤ l'). The null hypothesis H_{ij}: θ_i = θ_j is tested against the alternative A_{ij}: θ_i < θ_j for any 1 ≤ i < j ≤ k.

In the NPY' test the p-values are estimated from the studentized range distribution. In the NPT' test the p-values are estimated from the standard normal distribution.

Usage

chaAllPairsNashimotoTest(x, ...)

## Default S3 method:
chaAllPairsNashimotoTest(
  x,
  g,
  p.adjust.method = c("single-step", p.adjust.methods),
  ...
)

## S3 method for class 'formula'
chaAllPairsNashimotoTest(
  formula,
  data,
  subset,
  na.action,
  p.adjust.method = c("single-step", 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
`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 `NA`s. Defaults to `getOption("na.action")`.

Details

The type of test can be controlled via the argument p.adjust.method:

single.step: the NPY' test is performed.
none: the plain NPT' test is performed.

However, any method as available by p.adjust.methods can be selected for the adjustment of p-values estimated from the standard normal distribution.

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

Nashimoto, K., Wright, F.T., (2005) Multiple comparison procedures for detecting differences in simply ordered means. Comput. Statist. Data Anal. 48, 291–306.

Examples

## Example from Sachs (1997, p. 402)
x <- c(106, 114, 116, 127, 145,
       110, 125, 143, 148, 151,
       136, 139, 149, 160, 174)
g <- gl(3,5)
levels(g) <- c("A", "B", "C")
chackoTest(x , g)
chaAllPairsNashimotoTest(x, g, p.adjust.method = "single-step")

[Package PMCMRplus version 1.6.0 Index]