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

Human Decision Time in Uncertain Binary Choice

Decision time, also known as choice reaction time, has been frequently discussed in the field of psychology. The Hick–Hyman Law (HHL) has been a fundamental model that has revealed the quantitative relationship between the mean choice reaction time of human and the information entropy of stimuli. However, the HHL is only focused on rule-based behavior in which rules for selecting response according to stimulus are certain and neglects to model the knowledge-based behavior in which choices are uncertain and influenced by human belief. In this article, we explored the decision time related to one basic knowledge-based behavior—uncertain binary choice, where selections of response are determined by human belief degrees but not by stimuli uncertainties. Two experiments were conducted: one for verifying the HHL and the other for uncertain binary choice. The former (experiment) demonstrated the effectiveness of the HHL, and the latter one indicated that there is an exponential relationship existing between decision time and entropy of belief degree in uncertain binary choice. Moreover, data obtained from both experiments showed that the disturbance term of decision time should not be seen as probabilistic as existing studies have assumed, which highlighted the necessity and advantage of uncertain regression analysis.

Hick's law equivalent for reaction time to individual stimuli

Hick's law, one of the few law-like relationships involving human performance, expresses choice reaction time as a linear function of the mutual information between the stimulus and response events. However, since this law was first proposed in 1952, its validity has been challenged by the fact that it only holds for the overall reaction time (RT) across all the stimuli, and does not hold for the reaction time (RT_i ) for each individual stimulus. This paper introduces a new formulation in which RT_i is a linear function of (1) the mutual information between the event that stimulus i occurs and the set of all potential response events and (2) the overall mutual information for all stimuli and responses. Then Hick's law for RT follows as the weighted mean of each side of the RT_i equation using the stimulus probabilities as the weights. The new RT_i equation incorporates the important speed-accuracy trade-off characteristic. When the performance is error-free, RT_i becomes a linear function of two entropies as measures of stimulus uncertainty or unexpectancy. Reanalysis of empirical data from a variety of sources provide support for the new law-like relationship.