Attentional control over either of the two competing percepts of ambiguous stimuli revealed by a two-parameter analysis: means do not make the difference.

We studied distributions of perceptual rivalry reversals, as defined by the two fitted parameters of the Gamma distribution. We did so for a variety of bi-stable stimuli and voluntary control exertion tasks. Subjects' distributions differed from one another for a particular stimulus and control task in a systematic way that reflects a constraint on the describing parameters. We found a variety of two-parameter effects, the most important one being that distributions of subjects differ from one another in the same systematic way across different stimuli and control tasks (i.e., a fast switcher remains fast across all conditions in a parameter-specified way). The cardinal component of subject-dependent variation was not the conventionally used mean reversal rate, but a component that was oriented-for all stimuli and tasks-roughly perpendicular to the mean rate. For the Necker cube, we performed additional experiments employing specific variations in control exertion, suggesting that subjects have to a considerable extent independent control over the reversal rate of either of the two competing percepts.