A Generalized Kruskal-Wallis Test Incorporating Group Uncertainty with   Application to Genetic Association Studies
  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. 
Elif F. Acar and Lei Sun
stat.ME