Legal Sufficiency of Statistical Evidence

30 Pages Posted: 5 Sep 2018 Last revised: 31 May 2019

See all articles by Jonah B. Gelbach

Jonah B. Gelbach

University of California, Berkeley - School of Law

Bruce H. Kobayashi

George Mason University - Antonin Scalia Law School

Date Written: August 14, 2018

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.

Keywords: evidence, legal sufficiency, civil procedure, complex litigation, statistical evidence, Bayesian statistics, likelihood ratio, hypothesis testing

Suggested Citation

Gelbach, Jonah B. and Kobayashi, Bruce H., Legal Sufficiency of Statistical Evidence (August 14, 2018). George Mason Legal Studies Research Paper No. LS 18-29. Available at SSRN: https://ssrn.com/abstract=3238793 or http://dx.doi.org/10.2139/ssrn.3238793

Jonah B. Gelbach (Contact Author)

University of California, Berkeley - School of Law ( email )

215 Boalt Hall
Berkeley, CA 94720-7200
United States

Bruce H. Kobayashi

George Mason University - Antonin Scalia Law School ( email )

3301 Fairfax Drive
Arlington, VA 22201
United States
703-993-8034 (Phone)
703-993-8088 (Fax)

HOME PAGE: http://mason.gmu.edu/~bkobayas

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