My very brief experience with the review systems of conferences and journals has been that the statistics or any details are seldom checked thoroughly. The editors and reviewers only seem to have the time to evaluate the story, the overall picture and a few routine details, but never anything. Is that rather common? Because in that case, the responsibility for correctness of the papers seems largely up to the individual, their immediate labmates or supervisor, and more generally the department to ensure that everything is going well.