[R] Jonckheere-Terpstra test

[Kim Mouridsen]

The Jonckheere-Terpstra test is a distribution-free test for ordered
alternatives in a one-way layout. More specifically, assume

X_ij = m + t_j + e_ij,		i=1,...,n_j and j=1,...,k,

where the errors are idependent and identically distributed. Then you
can use the Jonckheere-Terpstra to test

H_0:    t_1=t_2=...=t_k
against
H_A:    t_1<=t_2<=...<=t_k,

where at least one of the inequalities is strict.

To my knowledge there is no R code for this test but the test statistic
is not too hard to calculate (you have to calculate some Mann-Whitney
counts) and the p-value can be found in a table - or in case you have
many observations you can use a large-sample approximation. 

The original article appeared in 
Biometrika, Vol. 41, No. 1/2. (Jun., 1954), pp. 133-145

But it is probably easier to read page 120-123 in
"Nonparametric statistical methods" by Hollander and Wolfe (1973) Wiley
& Sons.

A NOT-distribution-free alternative to this test is described in 
Biometrika, Vol. 72, No. 2. (Aug., 1985), pp. 476-480.

Kim.
 

-----Original Message-----
From: r-help-bounces at stat.math.ethz.ch
[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of
Arne.Muller at aventis.com
Sent: 5. oktober 2003 14:51
To: r-help at stat.math.ethz.ch
Subject: [R] Jonckheere-Terpstra test

Hello,

can anybody here explain what a Jonckheere-Terpstra test is and whether
it is
implemented in R? I just know it's a non-parametric test, otherwise I've
no
clue about it ;-( . Are there alternatives to this test?

	thanks for help,

	Arne

______________________________________________
R-help at stat.math.ethz.ch mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help