View source: R/frdAllPairsSiegelTest.R
frdAllPairsSiegelTest | R Documentation |
Performs Siegel and Castellan's all-pairs comparisons tests of Friedman-type ranked data.
frdAllPairsSiegelTest(y, ...)
## Default S3 method:
frdAllPairsSiegelTest(
y,
groups,
blocks,
p.adjust.method = p.adjust.methods,
...
)
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 |
p.adjust.method |
method for adjusting p values
(see |
... |
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, 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.
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.
Siegel, S., Castellan Jr., N. J. (1988) Nonparametric Statistics for the Behavioral Sciences. 2nd ed. New York: McGraw-Hill.
friedmanTest
, friedman.test
,
frdAllPairsExactTest
, frdAllPairsConoverTest
,
frdAllPairsNemenyiTest
, frdAllPairsMillerTest
## 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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