Figure 1
From: Second-generation PLINK: rising to the challenge of larger and richer datasets
2 × 2 contingency table log-frequencies. This is a plot of relative frequencies of 2 × 2 contingency tables with top row sum 1000, left column sum 40000, and grand total 100000, reflecting a low-MAF variant where the difference between the chi-square test and Fisher’s exact test is relevant. All such tables with upper left value smaller than 278, or larger than 526, have frequency smaller than 2−53 (dotted horizontal line); thus, if the obvious summation algorithm is used, they have no impact on the p-value denominator due to numerical underflow. (It can be proven that this underflow has negligible impact on accuracy, due to how rapidly the frequencies decay.) A few more tables need to be considered when evaluating the numerator, but we can usually skip at least 70%, and this fraction improves as problem size increases.