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A Generalized Kruskal–Wallis Test Incorporating Group Uncertainty with Application to Genetic Association Studies
Author(s) -
Acar Elif F.,
Sun Lei
Publication year - 2013
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/biom.12006
Subject(s) - mathematics , kruskal–wallis one way analysis of variance , statistics , kruskal's algorithm , test statistic , null hypothesis , generalization , robustness (evolution) , pearson's chi squared test , statistic , statistical hypothesis testing , combinatorics , mann–whitney u test , genetics , spanning tree , biology , mathematical analysis , gene
Summary Motivated by genetic association studies of SNPs with genotype uncertainty, we propose a generalization of the Kruskal–Wallis test that incorporates group uncertainty when comparing k samples. The extended test statistic is based on probability‐weighted rank‐sums and follows an asymptotic chi‐square distribution with k − 1 degrees of freedom under the null hypothesis. Simulation studies confirm the validity and robustness of the proposed test in finite samples. Application to a genome‐wide association study of type 1 diabetic complications further demonstrates the utilities of this generalized Kruskal–Wallis test for studies with group uncertainty. The method has been implemented as an open‐resource R program, GKW .