In Home Paramount Pest Control  v. Gibbs, (Del. Supr., Jan. 17, 2008), read opinion here, the Delaware Supreme Court addressed the judicial recusal standard in the context of a hearing officer for an administrative agency. Here is the quote that recites the two-part test for recusal and the reasoning behind the rule:

The requirement that judges be impartial is a fundamental
principle of the administration of justice …. As a matter of due
process, a litigant is entitled to neutrality on the part of the
presiding judge but the standards governing disqualification also
require the appearance of impartiality.
* * *
When faced with a claim of personal bias or prejudice
under [Canon 3 C(1) of the Delaware Code of Judicial Conduct]
the judge is required to engage in a two-part analysis. First, he
must, as a matter of subjective belief, be satisfied that he can
proceed to hear the cause free of bias or prejudice concerning that
party. Second, even if the judge believes that he has no bias,
situations may arise where, actual bias aside, there is the
appearance of bias sufficient to cause doubt as to the judge’s

This Court reviews the subjective part of the … test for abuse of discretion. We review de novo the objective determination of whether there is an appearance of bias.