We propose and evaluate a memory-based model of Hick's law, the approximately linear increase in choice reaction time with the logarithm of set size (the number of stimulus-response alternatives). According to the model, Hick's law reflects a combination of associative interference during retrieval from declarative memory and occasional savings for stimulusresponse repetitions due to non-retrieval. Fits to existing data sets show that the model accounts for the basic set-size effect, changes in the set-size effect with practice, and stimulus-response repetition effects that challenge the information-theoretic view of Hick's law. We derive the model's prediction of an interaction between set size, stimulus fan (the number of responses associated with a particular stimulus), and stimulus-response transition, which is subsequently tested and confirmed in two experiments. Collectively, the results support the core structure of the model and its explanation of Hick's law in terms of basic memory effects.
KeywordsHick's law; choice reaction time; memory; fan effect; cognitive modeling Choice reaction time (RT) has been of interest to cognitive psychologists for well over 50 years. In a typical choice RT paradigm, a set of stimuli is associated with a set of responses, usually with a one-to-one mapping of stimuli onto responses. A stimulus is presented on each trial and the task is to choose the corresponding response, with correct RT serving as the primary dependent measure. Research involving this paradigm has revealed that as set size (the number of stimulus-response alternatives) increases, RT becomes longer (e.g., Hick, 1952;Hyman, 1953;Merkel, 1885; for reviews, see Luce, 1986, Chapter 10;E. E. Smith, 1968;Teichner & Krebs, 1974;Welford, 1960). More specifically, there is an approximately linear increase in RT with the logarithm of set size (n):(1) Figure 1 shows fits of Equation 1 to four representative data sets. The close match between Equation 1 (or variants of it) and the empirical set-size effect has led to both being referred to interchangeably as Hick's law (after Hick, 1952). Hick's law seems to be one of the few "laws" that exist in cognitive psychology and it is a benchmark effect in the study of choice RT (Luce, 1986;E. E. Smith, 1968;Teichner & Krebs, 1974;Welford, 1960).Address correspondence to: Darryl W. Schneider, Department of Psychology, Carnegie Mellon University, Pittsburgh, PA 15213, USA, Phone: 1-412-334-7758, dws@cmu.edu. Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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