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’.
There is a brief summary of the authorities on when discourteous behaviours of RRT members can amount to a denial of natural justice by reason of apprehended bias, in AZAEY v Minister for Immigration and Border Protection  FCAFC 193.
On the facts in AZAEY, there was no apprehended bias. This was so, even though the Court found that on some occasions the Tribunal member did interrupt the Applicant on ‘a number of occasions’, was ‘incredulous’ towards the Applicant and raised her voice towards the Applicant. The Court also referred to a number of occasions in which the Applicant was crying, presumably as a result of the Tribunal member’s behaviour.
The Court concluded however, that when having regard to the transcript and recording of the RRT hearing as a whole, an informed person ‘would satisfactorily reach a conclusion that the Applicant had been afforded a hearing in which the Tribunal member was “open to persuasion”‘: . That is the ‘governing principle’ in relation to apprehended bias: see Ebner v Official Trustee in Bankruptcy  HCA 63, (2000) 205 CLR 337 at 344 to 345, cited in AZAEY at .