The danger of trial-by-trial knowledge of results in perceptual averaging studies

Revived interest in "intuitive statistics" (Peterson & Beach, 1967) is evident in recent studies concerning the ability of observers to estimate mean size for ensembles of lines or of circles. To put the recent studies in context, and to highlight a potential danger in providing trial-by-trial knowledge of results (KOR), brief contact with previous research is made and a new experiment is presented demonstrating the malleability of responding to KOR. Together, these suggest two perils of KOR. First, given that the nature and even the existence of a molar size-averaging operator are both controversial, the proper criterion average for determining KOR is unclear. Second, whatever the operation observers use in this task, its scope and algorithm need to emerge from data unbiased by KOR. A corollary scaling concern is noted for averaging of areal stimuli (perceived as a compression function of physical area) as an instance of the more general concern that perceptual scaling factors must be taken into account when psychological averaging processes are studied.