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Abstract: There are many cases and administrative proceedings in which statistical data obtained by observation or experiment are readily accepted as assisting in the proper resolution of disputed issues of fact. When courts or administrators confront scientific and statistical evidence in these proceedings, they are not always certain of how to weigh the evidence or whether they should, or must, rely on the standards for proof that scientists apply in evaluating statistical hypotheses.
In any case involving statistical proof, the proponent of the evidence understandably covets testimony that the data is "significant." Although there are grounds to question whether such testimony as to "significance" should even be admissible, this article confines attention to the relationship between the putative scientific standard of proof and the legal standards of proof. It describes these legal standards, first in the conventional language of the law and then in the terminology of statistical decision theory. Then it describes the technical concept of statistical significance and shows the impossibility, in general, of equating statistical significance with legally satisfactory proof. Hopefully this article will be the beginning of a clearer understanding of how statistical methods for measuring the probative force of data can help the trier of fact decide whether the proponent of the data has fulfilled the appropriate burden of persuasion. While Statistically significant results are nice to have, the mere fact that an expert states that data are "significant" does not necessarily mean that the evidence satisfies the applicable burden of persuasion. Nor does the fact that a scientist cannot certify data as "significant" imply that the evidence inevitably falls short of what the law requires. The process of judgment, in law as well as in science, is much richer than the recipes for statistical hypothesis tests reveal.
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