[east2west]

Exactly, numerical errors could easily have accounted for the difference between already tiny p-values. The point isn't that the smaller p-value isn't better than the bigger one, it is, but that small significance should have been attached to the difference.

This example is a gnome-wide genetic association study. Every genetic variations are tested, so at least 500K or more linear regressions were performed. This many statistical tests could lead to many false positives just by chance, so one must do multiple-testing corrections. The end result of multiple-testing correction is much bigger and therefore worse p-values. Hence the drive toward ridiculously tiny p-values.