PMCMRplus (version 1.9.12)

frdAllPairsSiegelTest: Siegel and Castellan's All-Pairs Comparisons Test for Unreplicated Blocked Data

Description

Performs Siegel and Castellan's all-pairs comparisons tests of Friedman-type ranked data.

Usage

frdAllPairsSiegelTest(y, ...)
# S3 method for default
frdAllPairsSiegelTest(
  y,
  groups,
  blocks,
  p.adjust.method = p.adjust.methods,
  ...
)

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.

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.

p.adjust.method

method for adjusting p values (see p.adjust).

...

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, Siegel and Castellan'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 standard normal distribution. Any method as implemented in p.adjust can be used for p-value adjustment.

References

Siegel, S., Castellan Jr., N. J. (1988) Nonparametric Statistics for the Behavioral Sciences. 2nd ed. New York: McGraw-Hill.

See Also

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

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)