frdAllPairsMillerTest {PMCMRplus}

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

Description

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

Usage

frdAllPairsMillerTest(y, ...)

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

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.

...

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, Miller'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 chi-square 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

Bortz J., Lienert, G. A., Boehnke, K. (1990) Verteilungsfreie Methoden in der Biostatistik. Berlin: Springer.

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

Wike, E. L. (2006), Data Analysis. A Statistical Primer for Psychology Students. New Brunswick: Aldine Transaction.

See Also

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