Legal Sufficiency of Statistical Evidence

Abstract

When are litigants' statistical estimates legally sufficient, given that courts use the preponderance of the evidence standard? We answer this question using Bayesian hypothesis testing and principles of federal procedural law, focusing on the common case of statistical estimation evidence from a normally distributed estimator. Our core result is that mathematical statistics and black-letter law combine to create a simple standard: statistical estimation evidence is legally sufficient when it fits the litigation position of the party relying on it. This means statistical estimation evidence is legally sufficient when the p-value is less than 0.5; equivalently, the preponderance standard is frequentist hypothesis testing with a significance level of just below 0.5. Finally, we show that conventional significance levels such as 0.05 require elevated standards of proof tantamount to clear-and-convincing or beyond-a-reasonable-doubt.