A Generalized Kruskal–Wallis Test Incorporating Group Uncertainty with Application to Genetic Association Studies

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 .