What is the legal test for disqualifying a district judge based on a bias or partiality motion?

2 Colacircio's reason for relying on these novel theories to disqualify the district judge, while expressly disclaiming reliance on the traditional bases for disqualification, 28 U.S.C. 144 and 455, is readily transparent: the "extrajudicial source" doctrine applicable to those statutes instructs that "judicial rulings alone almost never constitute a valid basis for a bias or partiality motion" and "[i]n and of themselves ... cannot possibly show reliance upon an extrajudicial source." Liteky v. United States, 510 U.S. 540, 555 1994 (emphasis added).