PMCMRplus (version 1.3.0)

chaAllPairsNashimotoTest: 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, \(\theta_m' - \theta_m \le \theta_j - \theta_i \le \theta_l' - \theta_l \qquad (l \le i \le m~\mathrm{and}~ m' \le j \le l')\). The null hypothesis H\(_{ij}: \theta_i = \theta_j\) is tested against the alternative A\(_{ij}: \theta_i < \theta_j\) for any \(1 \le i < j \le k\).

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

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.

References

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

See Also

Tukey, Normal, chackoTest

Examples

# NOT RUN {
## 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")
# }