# Changes

SKAT has been powerful detecting genes with rare variants having opposite directions in effect sizes. Meta-analysis statistic can also be re-constructed using single variant meta-analysis scores and their covariances $\mathbf{Q}=\mathbf{{U_{meta}}^T}\mathbf{W}\mathbf{U_{meta}}$.  As shown in Wu et. al, the null distribution of the $\mathbf{Q}$ statistic follows a mixture chi-sqaured distribution described as