What is the legal test for recusal of a judge in a civil matter?

Normally, there is no conflict between our duty as individual judges to appear impartial and our obligation to afford justice to all. In those cases in which there is a conflict, there is usually some method of ensuring that both goals can be accomplished within the normal procedures governing the operation of the judicial system. For example, a trial judge faced with such a conflict can recuse himself, and another trial judge can be substituted. So, too, a circuit judge can, normally, readily be replaced by another circuit judge or even by a district judge. There are, however, a few cases in which there is no mechanism for resolving the conflict in a manner that allows the court to honor both obligations fully. In such cases the obligation to do justice prevails and the "rule of necessity" applies. Under that rule, the court must hear the case and do justice even though an appearance of interest or impropriety may exist. See United States v. Will, 449 U.S. 200, 213-17, 101 S.Ct. 471, 480-82, 66 L.Ed.2d 392 (1981).