Abstract

The relationship between legal decision rules and thresholds of statistical significance is a well-known and studied phenomena in the academic literature. Moreover, this distinction has been recognized in law. For example, in Matrix v. Siracusano, the Court unanimously rejected the petitioner’s argument that the issue of materiality in a securities class action can be defined by the presence or absence of a statistically significant effect. However, in other contexts, thresholds based on fixed significance levels continue to be used as a legal standard. Our positive analysis demonstrates how a choice of either a statistical significance threshold or a legal standard represent alternative and often inconsistent ways to tradeoff error costs, and that thresholds based on fixed significance levels are not generally consistent with optimal legal rules. We also show how the two thresholds can be reconciled by replacing fixed significance levels with likelihood ratio
tests.