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.

中文翻译：

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希克定律等效于对个体刺激的反应时间

希克定律是少数涉及人类表现的类似定律的关系之一，它将选择反应时间表示为刺激和反应事件之间相互信息的线性函数。但是，由于该法于1952年首次提出，其有效性受到质疑的事实，它只适用于总反应时间（RT跨所有刺激），而并不适用于反应时间（RT_我）对每个个人刺激。本文介绍了一种新的公式，其中RT _i是 (1) 刺激i的事件之间的互信息的线性函数发生和所有潜在反应事件的集合和（2）所有刺激和反应的整体互信息。然后，RT 的希克定律遵循RT _i方程每一边的加权平均值，使用刺激概率作为权重。新的RT _i方程结合了重要的速度-精度权衡特性。当性能没有错误时，RT _i成为两个熵的线性函数，作为刺激不确定性或意外性的度量。对来自各种来源的经验数据的重新分析为新的类似法律的关系提供了支持。