jonckheere.test: Exact/permutation version of Jonckheere-Terpstra test
Description
Jonckheere-Terpstra test to test for ordered differences among classes
Usage
jonckheere.test(x, g, alternative = c("two.sided", "increasing",
"decreasing"), nperm=NULL)
Arguments
x, g
data and group vector
alternative
means are monotonic (two.sided), increasing, or
decreasing
nperm
number of permutations for the reference distribution.
The default is null in which case the permutation p-value is not
computed. Recommend that the user set nperm to be 1000 or higher if
permutation p-value is desired.
Details
jonckheere.test is the exact (permutation) version of the
Jonckheere-Terpstra test. It uses the statistic
$$\sum_{k<l} \sum_{ij} I(X_{ik} < X_{jl}) + 0.5 I(X_{ik} =
X_{jl}),$$ 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.
References
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.