Error Costs, Legal Standards of Proof, and Statistical Significance

The relationship between legal standards of proof and thresholds of statistical significance is a well-known and studied phenomenon in the academic literature. Moreover, the distinction between the two 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 imported from academic settings continue to be used as a legal standard of proof. Our positive analysis uses simple null and alternative hypotheses to demonstrate how statistical significance thresholds and legal standards of proof represent alternative approaches to balancing error costs. Within this framework of simple hypotheses, we show that thresholds based on fixed significance levels generally are not consistent with existing or optimal legal standards of proof. We also show how the statistical testing and legal standards of proof can be reconciled by replacing fixed significance-level hypothesis testing with likelihood ratio tests.