Exceptions to Hick's law: explorations with a response duration measure.

Abstract

Five experiments used a new response-duration measure in explorations of the conditions necessary for confirmation of Hick's law. Hick's law states that reaction time increases logarithmically with number of choices. Exceptions to the law, venerable as it is, have been reported. They have always included the following conditions: a verbal response; a familiar stimulus with a single dominant name; and a large number of practice trials. These conditions have carried a heavy explanatory burden in accounting for the anamolous results. The present studies use none of these conditions and yet manage to replicate the anamolous result of a very shallow slope across set size, a slope less than one-tenth the usual value. This was accomplished by using a novel task in which the initial component of the response is the same for all stimuli (depression of a single response key) but the termination of the response is different (different durations for each stimulus). Using this task, a slope in the neighborhood of 15 ms per bit of stimulus uncertainty is found, as compared with the usual value of about 150 ms. A number of possible explanations are examined. Among the most important are the possibilities that response overlap is the critical factor (i.e., duration errors overlap); possible stimuli are simply ignored when more than one is involved; and the duration decision is made after the reaction-time interval rather than during it. All three possibilities, as well as some others, are found to be inconsistent with the various experimental outcomes. Instead, a new theory of choice reaction time is presented, which emphasizes the nature of the S-R code that is assumed to represent various reaction-time tasks. This theory leads to a new "law" that is put forward as a replacement for Hick's law. It is RT = a + b(1 - N-1).