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Improved testing of species traits–environment relationships in the fourth‐corner problem
Author(s) -
ter Braak Cajo J. F.,
Cormont Anouk,
Dray Stéphane
Publication year - 2012
Publication title -
ecology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.144
H-Index - 294
eISSN - 1939-9170
pISSN - 0012-9658
DOI - 10.1890/12-0126.1
Subject(s) - permutation (music) , type i and type ii errors , statistics , mathematics , statistical hypothesis testing , ordination , type (biology) , table (database) , combinatorics , econometrics , algorithm , ecology , computer science , biology , data mining , physics , acoustics
The fourth‐corner problem entails estimation and statistical testing of the relationship between species traits and environmental variables from the analysis of three data tables. In a 2008 paper, S. Dray and P. Legendre proposed and evaluated five permutation methods for statistical significance testing, including a new two‐step testing procedure. However, none of these attained the correct type I error in all cases of interest. We solve this problem by showing that a small modification of their two‐step procedure controls the type I error in all cases. The modification consists of adjusting the significance level from to α or, equivalently, of reporting the maximum of the individual P values as the final one. The test is also applicable to the three‐table ordination method RLQ.

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