Sharpen statistical significance: Evidence thresholds and Bayes factors sharpened to Occam's razors

Abstract

Occam's razor suggests assigning more prior probability to a hypothesis corresponding to a simpler distribution of data than to a hypothesis with a more complex distribution of data, other things equal. An idealization of Occam's razor in terms of the entropy of the data distributions tends to favor the null hypothesis over the alternative hypothesis. As a result, lower p values are needed to attain the same level of evidence. A recently debated argument for lowering the significance level to 0.005 as the p value threshold for a new discovery and to 0.05 for a suggestive result would then support further lowering them to 0.001 and 0.01, respectively.