The test and authorities discussing factual permutations are discussed by Kenny J in VFAB v Minister for Immigration & Multicultural & Indigenous Affairs  FCA 872.
It is whether a fair-minded lay observer might reasonably apprehend that the Tribunal member might not have brought an impartial mind to the resolution of the question to be decided.
A particularly outrageous example is found in S233 of 2002  FMCA 39. See for example:
 It is also noteworthy that on that same page, at about point nine, that the turn that emerges from the text of the Tribunal members’ questioning of the applicant is, to say the least unfortunate, bearing on the sarcastic and I quote:
How can they possibly distribute these dissident leaflets in parks and cafes? How can that possibly happen? Do they walk around to people having picnics and say ‘will you please read this’? Do they interrupt someone in the middle of bowl of pho and say ‘Oh excuse me, just while you are having your pho would you please read this pamphlet’.