Exact Version of Jonckheere-Terpstra Test
Jonckheere-Terpstra test to test for ordered differences among classes.
JonckheereTerpstraTest(x, ...)
## Default S3 method:
JonckheereTerpstraTest(x, g, alternative = c("two.sided", "increasing", "decreasing"),
nperm = NULL, ...)
## S3 method for class 'formula'
JonckheereTerpstraTest(formula, data, subset, na.action, ...)x |
a numeric vector of data values, or a list of numeric data vectors. |
g |
a vector or factor object giving the group for the corresponding elements of x. Ignored if x is a list. |
alternative |
means are monotonic ( |
nperm |
number of permutations for the reference distribution.
The default is |
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 NAs. Defaults to |
... |
further argument to be passed to methods. |
JonckheereTerpstraTest is the exact (permutation) version of the Jonckheere-Terpstra test. It uses the statistic
∑_{k<l} ∑_{ij} I(X_{ik} < X_{jl}) + 0.5 I(X_{ik} = X_{jl}),
where i, j are observations in groups k and
l respectively. The asymptotic version is equivalent to
cor.test(x, g, method="k"). The exact calculation requires that there
be no ties and that the sample size is less than 100. When data are
tied and sample size is at most 100 permutation p-value is returned.
If x is a list, its elements are taken as the samples to be compared, and hence have to be numeric data vectors.
In this case, g is ignored, and one can simply use JonckheereTerpstraTest(x) to perform the test.
If the samples are not yet contained in a list, use JonckheereTerpstraTest(list(x, ...)).
Otherwise, x must be a numeric data vector, and g must be a vector or factor object of the
same length as x giving the group for the corresponding elements of x.
The function was previously published as jonckheere.test() in the clinfun package and has been
integrated here without logical changes. Some argument checks and a formula interface were added.
Venkatraman E. Seshan <seshanv@mskcc.org>, minor adaptations Andri Signorell
Jonckheere, A. R. (1954). A distribution-free k-sample test again ordered alternatives. Biometrika 41:133-145.
Terpstra, T. J. (1952). The asymptotic normality and consistency of Kendall's test against trend, when ties are present in one ranking. Indagationes Mathematicae 14:327-333.
set.seed(1234) g <- ordered(rep(1:5, rep(10,5))) x <- rnorm(50) + 0.3 * as.numeric(g) JonckheereTerpstraTest(x, g) x[1:2] <- mean(x[1:2]) # tied data JonckheereTerpstraTest(x, g) JonckheereTerpstraTest(x, g, nperm=5000) # Duller, S. 222 coffee <- data.frame( time=c( 447,396,383,410, 438,521,468,391,504,472, 513,543,506,489,407), grp=Untable(c(4,6,5), type="ordered")[,1] ) # the formula interface: JonckheereTerpstraTest(time ~ grp, data=coffee)
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