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A ratio‐to‐control Williams‐type test for trend
Author(s) -
Hothorn Ludwig A.,
Djira Gemechis D.
Publication year - 2010
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.464
Subject(s) - confidence interval , type i and type ii errors , statistics , test (biology) , contrast (vision) , interpretation (philosophy) , mathematics , extension (predicate logic) , homogeneous , multiple comparisons problem , computer science , econometrics , artificial intelligence , paleontology , combinatorics , biology , programming language
Under certain conditions, many multiple contrast tests based on the difference of treatment means can also be conveniently expressed in terms of ratios. In this paper, a Williams test for trend is defined as ratios‐to‐control for ease of interpretation and to obtain directly comparable confidence intervals. Simultaneous confidence intervals for percentages are particularly helpful for interpretations in the case of multiple endpoints. Methods for constructing simultaneous confidence intervals are discussed under both homogeneous and heterogeneous error variances. This approach is available in the R extension package mratios . The proposed method is used to test for trend in an immunotoxicity study with several endpoints as an example. Copyright © 2010 John Wiley & Sons, Ltd.