What is the test for establishing a standard of proof?

The purpose of a standard of proof is to instruct a fact finder concerning the degree of confidence our society thinks the fact finder should have in the correctness of factual conclusions for a particular type of adjudication, In Re Winship, 397 U.S. 358, 90 S.Ct. 1068, 25 L.Ed.2d 368. It allocates the risk of error between litigants and the relative importance attached to the ultimate decision of the fact finder. See Addington v. Texas, 441 U.S. 418, 99 S.Ct. 1804, 60 L.Ed.2d 323.