http://www.eli.pdx.edu/erc/handouts/proof.html
1. "Beyond a reasonable doubt" - used in criminal cases
"The test is one of reasonable doubt. A reasonable doubt is a doubt based upon reason and common sense -- the kind of doubt that would make a reasonable person hesitate to act. Proof beyond a reasonable doubt must, therefore, be proof of such a convincing character that you would be willing to rely and act upon it unhesitatingly in the most important of your own affairs. A reasonable doubt exists whenever, after careful and impartial consideration of all the evidence in the case, the jurors do not feel convinced to a moral certainty that a defendant is guilty of the charge."
Federal Jury Instructions - See Devitt & Blackmar, Section 11.01
2. "Clear and Convincing Evidence" - used in fraud cases
See Collins Securities Corp v. SEC, 562 F.2d 820 (D.C. Cir. 1977); See Gellhorn, p. 270.
The trier of fact must believe that it is highly probable that the facts are true or exist; while it is not necessary to believe to the point of almost certainty, or beyond a reasonable doubt, or that they certainly are true or exist; yet it is not sufficient to believe that it is merely more probable that they are true or exist than it is that they are false or do not exist.
3. Preponderance of the Evidence - Used in civil cases
The trier of fact must believe that it is more probable that the fact is true or exists than it is that it does not exist. See Gellhorn, p. 270 & Oregon Jury Instructions 22.02
4. Substantial Evidence - Use in most administrative cases
More than a mere scintilla. It means such relevant evidence as a reasonable mind might accept as adequate to support a conclusion.
See Richardson v. Perales, 402 U.S. 389; Universal Camera Corp. v. NLRB, 340 U.S. 474. See Gellhorn, pp. 258, 259, 737
5. A mere scintilla of Evidence- Used some old administrative cases
Enough evidence to create a suspicion of the existence of a fact.
See Universal Camera y, NLRB, supra.