frdAllPairsNemenyiTest {PMCMRplus}

Nemenyi's All-Pairs Comparisons Test for Unreplicated Blocked Data

Description

Performs Nemenyi's all-pairs comparisons tests of Friedman-type ranked data.

Usage

frdAllPairsNemenyiTest(y, ...)

## Default S3 method:
frdAllPairsNemenyiTest(y, groups, blocks, ...)

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

Arguments

y

a numeric vector of data values, or a list of numeric data vectors.

groups

a vector or factor object giving the group for the corresponding elements of "x". Ignored with a warning if "x" is a list.

blocks

a vector or factor object giving the block for the corresponding elements of "x". Ignored with a warning if "x" is a list.

formula

a formula of the form a ~ b | c where a, b and c give the data values and the corresponding groups and blocks, respectively.

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").

...

further arguments to be passed to or from methods.

Details

For all-pairs comparisons in a two factorial unreplicated complete block design with non-normally distributed residuals, Nemenyi's test can be performed on Friedman-type ranked data.

A total of m = k ( k -1 )/2 hypotheses can be tested. The null hypothesis, H_{ij}: \theta_i = \theta_j, is tested in the two-tailed case against the alternative, A_{ij}: \theta_i \ne \theta_j, ~~ i \ne j.

The p-values are computed from the studentized range 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

Demsar, J. (2006) Statistical comparisons of classifiers over multiple data sets, Journal of Machine Learning Research 7, 1–30.

Miller Jr., R. G. (1996) Simultaneous statistical inference. New York: McGraw-Hill.

Nemenyi, P. (1963), Distribution-free Multiple Comparisons. Ph.D. thesis, Princeton University.

Sachs, L. (1997) Angewandte Statistik. Berlin: Springer.

See Also

friedmanTest, friedman.test, frdAllPairsExactTest, frdAllPairsConoverTest, frdAllPairsMillerTest, frdAllPairsSiegelTest

Examples

 ## Sachs, 1997, p. 675
 ## Six persons (block) received six different diuretics
 ## (A to F, treatment).
 ## The responses are the Na-concentration (mval)
 ## in the urine measured 2 hours after each treatment.
 ##
 y <- matrix(c(
 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92,
 23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45,
 26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72,
 32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23,
 26.65),nrow=6, ncol=6,
 dimnames=list(1:6, LETTERS[1:6]))
 print(y)
 friedmanTest(y)

 ## Eisinga et al. 2017
 frdAllPairsExactTest(y=y, p.adjust = "bonferroni")

 ## Conover's test
 frdAllPairsConoverTest(y=y, p.adjust = "bonferroni")

 ## Nemenyi's test
 frdAllPairsNemenyiTest(y=y)

 ## Miller et al.
 frdAllPairsMillerTest(y=y)

 ## Siegel-Castellan
 frdAllPairsSiegelTest(y=y, p.adjust = "bonferroni")

 ## Irrelevant of group order?
 x <- as.vector(y)
 g <- rep(colnames(y), each = length(x)/length(colnames(y)))
 b <- rep(rownames(y), times = length(x)/length(rownames(y)))
 xDF <- data.frame(x, g, b) # grouped by colnames

 frdAllPairsNemenyiTest(xDF$x, groups = xDF$g, blocks = xDF$b)
 o <- order(xDF$b) # order per block increasingly
 frdAllPairsNemenyiTest(xDF$x[o], groups = xDF$g[o], blocks = xDF$b[o])
 o <- order(xDF$x) # order per value increasingly
 frdAllPairsNemenyiTest(xDF$x[o], groups = xDF$g[o], blocks = xDF$b[o])

 ## formula method (only works for Nemenyi)
 frdAllPairsNemenyiTest(x ~ g | b, data = xDF)