What is the test for a judge to determine whether or not the evidence was improperly admitted?

14 As noted by Lord Hewart, C.J., in Sussex Justices, there is a long line of cases supporting this principle, including Walker v. Frobisher, 6 VES. Jun. 70 May 7, 1801, where, at p. 944, the Lord Chancellor [Eldon] held: ...A Judge must not take upon himself to say, whether evidence improperly admitted had or had not an effect upon his mind. The award may have done perfect justice: but upon general principles it cannot be supported.

15 In Race v. Anderson et al, [1886] 14 O.A.R. 213, Hagarty, C.J.O., held, at p. 216: No principle is more important to be preserved intact than that which declares that every referee must scrupulously hold the balance evenly between litigant parties, and to hear nothing and know nothing (so far as is possible) urged or presented to him for or against one of the parties in the absence of the other, or without that other having the opportunity of knowing or answering it.