DescTools (version 0.99.37)

JonckheereTerpstraTest: Exact Version of Jonckheere-Terpstra Test

Description

Jonckheere-Terpstra test to test for ordered differences among classes.

Usage

JonckheereTerpstraTest(x, …)
# S3 method for default
JonckheereTerpstraTest(x, g, alternative = c("two.sided", "increasing", "decreasing"), 
                       nperm = NULL, …)
# S3 method for formula
JonckheereTerpstraTest(formula, data, subset, na.action, …)

Arguments

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 (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. It's recommended to set nperm to 1000 or higher if permutation p-value is desired.

formula

a formula of the form lhs ~ rhs where lhs gives the data values and rhs the corresponding groups.

data

an optional matrix or data frame (or similar: see model.frame) containing the variables in the formula formula. By default the variables are taken from environment(formula).

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 getOption("na.action").

…

further argument to be passed to methods.

Details

JonckheereTerpstraTest 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.

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.

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 <- 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)
# }