Incentive-Compatible Critical Values

Statistically significant results are more rewarded than insignificant ones, so researchers have the incentive to pursue statistical significance. Such p-hacking reduces the informativeness of hypothesis tests by making significant results much more common than they are supposed to be in the absence of true significance. To address this problem, we construct critical values of test statistics such that, if these values are used to determine significance, and if researchers optimally respond to these new significance standards, then significant results occur with the desired frequency. Such incentive-compatible critical values allow for p-hacking so they are larger than classical critical values. Using evidence from the social and medical sciences, we find that the incentive-compatible critical value for any test and any significance level is the classical critical value for the same test with approximately one fifth of the significance level -- a form of Bonferroni correction. For instance, for a z-test with a significance level of 5%, the incentive-compatible critical value is 2.31 instead of 1.65 if the test is one-sided and 2.57 instead of 1.96 if the test is two-sided.