JonckheereTerpstraTest {DescTools} | R Documentation |

## Exact Version of Jonckheere-Terpstra Test

### Description

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

### Usage

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

`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 |

`exact` |
logical, defining if the exact test should be calculated. If left to |

`...` |
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`

.

### Note

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.

### Author(s)

Venkatraman E. Seshan <seshanv@mskcc.org>, minor adaptations Andri Signorell

### 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

```
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 <- list(
c_4=c(447,396,383,410),
c_2=c(438,521,468,391,504,472),
c_0=c(513,543,506,489,407))
# the list interface:
JonckheereTerpstraTest(coffee)
# the formula interface
breaking <- data.frame(
speed=c(20,25,25,25,25,30,30,30,35,35),
distance=c(48,33,59,48,56,60,101,67,85,107))
JonckheereTerpstraTest(distance ~ speed, breaking, alternative="increasing")
```

*DescTools*version 0.99.54 Index]