# [R] coin package (conditional inference / permutation): parameter teststat

From: Paulo Barata <pbarata_at_infolink.com.br>
Date: Sun, 20 Jul 2008 20:16:57 -0300

Dear R-list members,

This is in fact a question about statistics, not directly about the R software.

The coin package, for conditional inference through permutation methods, has as it main function the function independence_test. One of its parameters is teststat, about which the package documentation says:

teststat: "a character, the type of test statistic to be applied:   either a standardized scalar test statistic (scalar), or   a maximum type statistic (max) or a quadratic form (quad).

My current problem is a two-sample (two-group) one, with multivariate response consisting entirely of continuous numerical observations.

Would someone please point me to references indicating the relative merits of the "max" and "quad" test statistics in this case?

The pdf document "Implementing a Class of Permutation Tests: The coin Package", by Hothorn et al., which comes with the package, says on page 5 that "In the multivariate case (pq > 1), a maximum-type statistic (...) is appropriate". But no reasons or references are provided.

P. Good, Permutation, Parametric, and Bootstrap Tests of Hypotheses. 3rd. ed. (Springer), says on page 180 (Section 9.4.4, Which Statistic?) [my comments in brackets]:

"We've now considered three multivariate test statistics for   testing hypothesis based on one or two samples. Which one should   we use? To detect a simultaneous shift in the means of several   variables, use Hotelling's T2 [a kind of 'quad' test statistics];   to detect a shift in any of several variables, use the maximum t   [a kind of 'max' test statistics] (...)"

But again, no reasons or references are provided.

So, I would like to know if anyone could indicate me references discussing the relative merits of the "max" and "quad" test statistics, in the case of a two-sample problem with continuous multivariate responses, when using permutation tests.

Just for information, I currently use R 2.7.1 running on Windows XP. The coin package is version 0.6-9 (5 May 2008).

Thank you very much.

Regards,

Paulo Barata

Paulo Barata
Fundacao Oswaldo Cruz
Rua Leopoldo Bulhoes 1480 - 8A
21041-210 Rio de Janeiro - RJ
Brazil