Evaluating performance in continuous experiments with feedback to subjects

Consider an experiment in which a subject guesses repeatedly at a randomly chosen target on a continuum. To guarantee a positive probability of success, the continuum is partitioned into a finite but large number of segments. The subject is given directional feedback. General guessing strategies are characterized, and an optimal strategy is identified. The hypothesis that the subject's performance can be explained by chance alone is of interest in such experiments. A test is developed based on comparing the subject's performance to expected performance using the optimal strategy. A skill-scoring procedure is developed for assessing a subject's performance in light of the strategy used, and a test based on skill-scoring is advanced.Research by the first author is supported in part by the Air Force Office of Scientific Research under grant AFOSR 77-3180.The authors wish to thank the referees for remarks that led to improvements in both content and clarity.