clinfun (version 1.0.15)

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.

Examples

# NOT RUN {
  set.seed(1234)
  g <- rep(1:5, rep(10,5))
  x <- rnorm(50)
  jonckheere.test(x+0.3*g, g)
  x[1:2] <- mean(x[1:2]) # tied data
  jonckheere.test(x+0.3*g, g)
  jonckheere.test(x+0.3*g, g, nperm=5000)
# }