Millers's All-Pairs Comparisons Test for Unreplicated Blocked Data
Performs Miller's all-pairs comparisons tests of Friedman-type ranked data.
frdAllPairsMillerTest(y, ...) ## Default S3 method: frdAllPairsMillerTest(y, groups, blocks, ...)
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 |
... |
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, 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}: 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 chi-square 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.
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.
## 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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