The roles of stimulus and response uncertainty in forced-choice performance: an amendment to Hick/Hyman Law

Abstract

Hick/Hyman Law describes one of the core phenomena in the study of human information processing: mean response time is a linear function of average uncertainty. In the original work of Hick, (1952) and Hyman, (1953), along with many follow-up studies, uncertainty regarding the stimulus and uncertainty regarding the response were confounded such that the relative importance of these two factors remains mostly unknown. The present work first replicates Hick/Hyman Law with a new set of stimuli and then goes on to separately estimate the roles of stimulus and response uncertainty. The results demonstrate that, for a popular type of task-visual stimuli mapped to vocal responses-response uncertainty accounts for a majority of the effect. The results justify a revised expression of Hick/Hyman Law and place strong constraints on theoretical accounts of the law, as well as models of response selection in general.

An information-theoretic perspective on the costs of cognition

“…same button presses, leading to 8 stimuli for 4 button presses), H(p 0 (y)) remains constant but reaction times increase, and they do so linearly with H(p 0 (x)) (Wifall et al, 2016). A similar increase in reaction time was reported in other tasks in which the complexity of the stimulus varies, while the number of response choices remains constant (Fan, 2014;Fan et al, 2008).…”

“…The present paper differs from this earlier treatment foremost by its focus on effort costs. In addition, we attempted at being more general, by adding the cost of perceptual processing, which is necessary to account for known behavioural results (Fan et al, 2008;Wifall et al, 2016) and by introducing ratedistortion theory. We also tried to clarify the formalism of the model by spelling out the different potential sources of cost.…”

Effects of average uncertainty and trial-type frequency on choice response time: A hierarchical extension of Hick/Hyman Law

“…These include the finding that the slope, b, of Hick/Hyman Law depends on both practice (e.g., Mowbray & Rhoades, 1959) and stimulus-response compatibility (e.g., Teichner & Krebs, 1974) and can even be zero when ideomotor mappings are used (e.g., Leonard, 1959); a similar interaction between average uncertainty and Simon congruence (e.g., Stoffels, van der Molen, & Keuss, 1989); and the independence of uncertainty and repetition effects (e.g., Kornblum, 1967). More recently, Wifall, Hazeltine, and Mordkoff (2016) have presented a revised version of Hick/Hyman Law that includes separate values of b and H for stimulus and response uncertainty (for situations under which the number or frequency of the stimuli and responses are not confound), but even this should be viewed as an expansion of the law, as opposed to a falsification. However, one serious limitation of Hick/ Hyman Law remains unresolved.…”

Effects of Frequency Distribution on Linear Menu Performance

“…skewed distributions are faster to select), it is unclear how it can be applied to individual item selection time. The original Hick's [13] and Hyman's [15] experiments only concerned the whole distribution, yet later studies [6,25] have applied HHL to individual item selection time: The former claimed that "decision time depends on the entropy of each item" T = a + b × (−log 2 (p i )) [6] and the latter introduced −log 2 (p i ) as "surprisal value for a particular trial" [25]. However, there has been no validation for this application.…”

“…More precisely, HHL indicates that response time is a linear function of H, the weighted surprisal value (also called average uncertainty) [25], H = −∑ p i × log 2 (p i ) with p i is the probability of appearance of an item. While HHL may reflect the phenomenon observed for the average menu selection time (i.e.…”