DescTools (version 0.99.8.1)

JonckheereTerpstraTest: Exact Version of Jonckheere-Terpstra Test

Description

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

Usage

JonckheereTerpstraTest(x, ...)

## S3 method for class 'default':
JonckheereTerpstraTest(x, g, alternative = c("two.sided", "increasing", "decreasing"), 
                       nperm = NULL, ...)

## S3 method for class 'formula':
JonckheereTerpstraTest(formula, data, subset, na.action, \dots)

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_{kcor.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

Run this code
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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