A note on the simultaneous computation of thousands of Pearson's X2-Statistics

In genetic association studies, important and common goals are the identification of single nucleotide polymorphisms (SNPs) showing a distribution that differs between several groups and the detection of SNPs with a coherent pattern. In the former situation, tens of thousands of SNPs should be tested, whereas in the latter case typically several ten SNPs are considered leading to thousands of statistics that need to be computed. A test statistic appropriate for both goals is Pearson’s χ2-statistic. However, computing this (or another) statistic for each SNP or pair of SNPs separately is very time-consuming. In this article, we show how simple matrix computation can be employed to calculate the χ2-statistic for all SNPs simultaneously.