The amount of evidence which a plaintiff (or prosecuting attorney, in a criminal case) must present in a trial in order to win is called the standard of proof. Different cases require different standards of proof depending on what is at stake. The common standards are:
Beyond a reasonable doubt (criminal cases)--for a criminal defendant to be convicted of a crime, the prosecutor must prove her case to the point that the jurors have no reasonable doubts in their minds that the defendant did whatever he is charged with having done.
Clear and convincing evidence (civil cases involving the potential loss of important interests such as the termination of parental rights)--for a party to prove a case under this standard, she must show something more than it is more likely than not, but not as much as beyond a reasonable doubt. No legal scholar has ever been able to define clear and convincing evidence more precisely than that.
Preponderance of the evidence (most civil cases including fault divorces)--preponderance of the evidence generally means that a party will win if she can show that it is more likely than not that her contention is true.
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