  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.
