Nemenyi's All-Pairs Comparisons Test for Unreplicated Blocked Data
Performs Nemenyi's all-pairs comparisons tests of Friedman-type ranked data.
frdAllPairsNemenyiTest(y, ...) ## Default S3 method: frdAllPairsNemenyiTest(y, groups, blocks, ...) ## S3 method for class 'formula' frdAllPairsNemenyiTest(formula, data, subset, na.action, ...)
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 |
blocks |
a vector or factor object giving the block for the
corresponding elements of |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see
|
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 |
... |
further arguments to be passed to or from methods. |
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}: 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 studentized range distribution.
A list with class "PMCMR" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
lower-triangle matrix of the p-values for the pairwise tests.
a character string describing the alternative hypothesis.
a character string describing the method for p-value adjustment.
a data frame of the input data.
a string that denotes the test distribution.
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.
## 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)
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