After an experiment has been completed and analyzed, a trend may be observed that is “not quite significant”. Sometimes in this situation, researchers incrementally grow their sample size N in an effort to achieve statistical significance. This is especially tempting in situations when samples are very costly or time-consuming to collect, such that collecting an entirely new sample larger than N would be prohibitive. Such post-hoc sampling or “N-hacking” is condemned, however, because it leads to an excess of false positive results.
In this study, the authors used Monte-Carlo simulations to show why and how incremental sampling causes false positives, but also to challenge the claim that it necessarily produces alarmingly high false positive rates. Contrary to widespread belief, the authors propose that collecting additional samples to resolve a borderline P value is not invalid, and can confer previously unappreciated advantages for efficiency and positive predictive value.
See also Commentary I in this Newsletter for further discussion.