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 ) for each individual stimulus. This paper introduces a new formulation in which RT 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 equation using the stimulus probabilities as the weights. The new RT equation incorporates the important speed-accuracy trade-off characteristic. When the performance is error-free, RT 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.