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On Distance‐Based Permutation Tests for Between‐Group Comparisons
Author(s) -
Reiss Philip T.,
Stevens M. Henry H.,
Shehzad Zarrar,
Petkova Eva,
Milham Michael P.
Publication year - 2010
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2009.01300.x
Subject(s) - permutation (music) , multivariate statistics , extension (predicate logic) , equivalence (formal languages) , multivariate analysis of variance , multivariate analysis , set (abstract data type) , data set , resampling , computer science , statistics , mathematics , multiple comparisons problem , algorithm , data mining , discrete mathematics , physics , acoustics , programming language
Summary Permutation tests based on distances among multivariate observations have found many applications in the biological sciences. Two major testing frameworks of this kind are multiresponse permutation procedures and pseudo‐ F tests arising from a distance‐based extension of multivariate analysis of variance. In this article, we derive conditions under which these two frameworks are equivalent. The methods and equivalence results are illustrated by reanalyzing an ecological data set and by a novel application to functional magnetic resonance imaging data.