What is the test to apply in determining whether juror misconduct requires a judgment to be set aside?

We then stated the test to apply in determining whether juror misconduct requires the judgment be set aside: "A judgment adverse to a defendant in a [9 Cal.4th 651] criminal case must be reversed or vacated 'whenever ... the court finds a substantial likelihood that the vote of one or more jurors was influenced by exposure to prejudicial matter relating to the defendant or to the case itself that was not part of the trial record on which the case was submitted to the jury.' [Citations.] ... [p] 'The ultimate issue of influence on the juror is resolved by reference to the substantial likelihood test, an objective standard. In effect, the court must examine the extrajudicial material and then judge whether it is inherently likely to have influenced the juror.' [Citation.]" (People v. Marshall, supra, 50 Cal.3d at pp. 950-951, 269 Cal.Rptr. 269, 790 P.2d 676, italics added.) We noted that this prejudice analysis is "different from, and indeed less tolerant than, 'harmless-error analysis' for ordinary error at trial. The reason is as follows. Any deficiency that undermines the integrity of a trial--which requires a proceeding at which the defendant, represented by counsel, may present evidence and argument before an impartial judge and jury--introduces the taint of fundamental unfairness and calls for reversal without consideration of actual prejudice. [Citation.] Such a deficiency is threatened by jury misconduct. When the misconduct in question supports a finding that there is a [889 P.2d 996] substantial likelihood that at least one juror was impermissibly influenced to the defendant's detriment, we are compelled to conclude that the integrity of the trial was undermined:

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