What is the legal test for disqualification of a judge for bias?

Under the due process clause of the federal Constitution, "while a showing of actual bias is not required for judicial disqualification under the due process clause, neither is the mere appearance of bias sufficient. Instead, based on an objective assessment of the circumstances in the particular case, there must exist '"the probability of actual bias on the part of the judge or decision maker [that] is too high to be constitutionally tolerable."' [Citation.] Where only the appearance of bias is at issue, a litigant's recourse is to seek disqualification under state disqualification statutes: 'Because the codes of judicial conduct provide more protection than due process requires, most disputes over disqualification will be resolved without resort to the Constitution.'" (People v. Freeman (2010) 47 Cal.4th 993, 996.)

Under Code of Civil Procedure section 170.1, subdivision (a)(6)(A), a judge must be disqualified if "the judge believes there is a substantial doubt as to his or her capacity to be impartial" (id., subd. (ii)) or a "person aware of the facts might reasonably entertain a doubt that the judge would be able to be impartial" (id., subd. (iii)). For example, if a trial court, in resolving disputed issues of fact, harbors "preconceptions about the parties because of their gender," these perceptions may prevent one party from receiving a fair trial. (In re Marriage of Iverson (1992) 11 Cal.App.4th 1495, 1499, disapproved on another ground in People v. Freeman, supra, 47 Cal.4th at pp. 1006-1007, fn. 4.) On the other hand, "the mere fact a judicial officer rules against a party does not show bias." (In re Marriage of Tharp (2010) 188 Cal.App.4th 1295, 1328.) "[L]itigants and attorneys sometimes manifest their emotional pique at a decision by blaming the judge for being biased. This type of accusation appears more frequently in the family law arena than any other area of law. The accuser's description of the questioned decision is at best incomplete and at worst self-servingly inaccurate." (Id. at p. 1326.)