frdAllPairsSiegelTest {PMCMRplus} | R Documentation

## 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, ...)

    ## Default S3 method:
    frdAllPairsSiegelTest(
      y,
      groups,
      blocks,
      p.adjust.method = p.adjust.methods,
      ...
    )

### 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}: θ_i = θ_j, is tested in the two-tailed case against the alternative, A_{ij}: θ_i \ne θ_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.

### 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

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)

[Package PMCMRplus version 1.6.1 Index]