Hick’s law: Its limit is 3 bits

Longstreth, Langdon E.

doi:10.3758/bf03334845

Cited by 13 publications

(8 citation statements)

References 9 publications

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“…Based on these results, Seibel (1963) suggested that the linear relationship between RT and the logarithm of set size held in the range of two to eight alternatives, but not beyond that range. Longstreth (1988) arrived at a similar conclusion based on experiments involving numerical stimuli and keypress responses. In his Experiment 1, set size was varied from 2 to 21 alternatives, with most sets consisting of one-and two-digit numbers (e.g., 4, 7 and 47 were the stimuli in a set of size 3) that required single-and double-keypress responses, respectively.…”

Section: Very Large Set Sizesmentioning

confidence: 72%

“…Longstreth (1988) arrived at a similar conclusion based on experiments involving numerical stimuli and keypress responses. In his Experiment 1, set size was varied from 2 to 21 alternatives, with most sets consisting of one- and two-digit numbers (e.g., 4, 7 and 47 were the stimuli in a set of size 3) that required single- and double-keypress responses, respectively.…”

Section: Additional Challenges To Hick’s Lawmentioning

confidence: 72%

“…In a reply, Longstreth and Alcorn (1987) continued to favor the power function, regarding fit differences to be small and countering Welford’s other criticisms. Longstreth (1988) also argued that the power function was superior to the logarithmic function in accounting for data from experiments that included very large set sizes. In a commentary on Longstreth’s (1988) paper, Kvålseth (1989) reiterated some of Welford’s key points, highlighted an error in the derivation of the power function and discussed how the function could be extended to accommodate unequal stimulus probabilities and repetition effects.…”

Section: Additional Challenges To Hick’s Lawmentioning

confidence: 99%

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Hick’s law for choice reaction time: A review

Proctor

Schneider

2018

Quarterly Journal of Experimental Psychology

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In 1952, W. E. Hick published an article in the Quarterly Journal of Experimental Psychology, "On the rate of gain of information." It played a seminal role in the cognitive revolution and established one of the few widely acknowledged laws in psychology, relating choice reaction time to the number of stimulus-response alternatives (or amount of uncertainty) in a task. We review the historical context in which Hick conducted his study and describe his experiments and theoretical analyses. We discuss the article's immediate impact on researchers, as well as challenges to and shortcomings of Hick's law and his analysis, including effects of stimulus-response compatibility, practice, very large set sizes and sequential dependencies. Contemporary modeling developments are also described in detail. Perhaps most impressive about Hick's law is that it continues to spawn research efforts to the present and that it is regarded as a fundamental law of interface design for human-computer interaction using technologies that did not exist at the time of Hick's research.

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Section: Very Large Set Sizesmentioning

confidence: 72%

Section: Additional Challenges To Hick’s Lawmentioning

confidence: 72%

Section: Additional Challenges To Hick’s Lawmentioning

confidence: 99%

See 1 more Smart Citation

Hick’s law for choice reaction time: A review

Proctor

Schneider

2018

Quarterly Journal of Experimental Psychology

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“…They submitted a power curve as a replacement for fitting the data: In response to Longstreth et al's model, Welford (1987) pointed out that when the model is applied to certain data sets, negative intercepts are derived, which is illogical for the dependent measure of time, and that the equation predicts a decreasing RT variability as a function of the number of alternatives, when empirically, the opposite has been observed. Longstreth and Alcorn (1987) offered their rebuttal but Longstreth (1988) may have relented when he conceded that the linearity as predicted by the law is true but is bounded by an upper limit of 3 bits.…”

Section: Theoretical Developmentsmentioning

confidence: 95%

Information Theoretic Models of HCI: A Comparison of the Hick-Hyman Law and Fitts' Law

Seow¹

2005

Human-Comp. Interaction

102

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The Hick-Hyman Law and Fitts' Law are two surviving human performance principles based on Shannon and Weaver's (1949) Information Theory. In the early 1980s, Card, Moran, and Newell (1983) presented the laws as design principles for developers to maximize usability in the design of human-computer interfaces. A search of the current human-computer interaction (HCI) literature, however, will reveal that the Hick-Hyman Law failed to gain momentum in the field of HCI, whereas Fitts' Law received, and continues to receive, substantial attention. This article begins with a discussion the common information theoretical concepts of the two laws, and then examines each law with respect to its origins, theoretical formulation, theoretical development, research, and applications and examines the possible contributing factors responsible for the failure of Hick-Hyman Law to gain momentum in the field.

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“…Using Hick's (logarithmic) law as an example (Hick, 1952), the lack of an asymptote as the number of responses increases forces the bizarre prediction that response times will become infinitely long in the continuous case. Naturally, this type of prediction does not pan out in empirical response time data, as violations of Hick's law have been observed when there are (substantially) more than eight alternatives (Longstreth, 1988;Seibel, 1963).…”

Section: Extrapolating To the Continuummentioning

confidence: 99%

A unified theory of discrete and continuous responding

Kvam¹,

Marley²,

Heathcote³

2021

Preprint

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Understanding the cognitive processes underlying choice requires theories that can disentangle the representation of stimuli from the processes that map these representations onto observed responses. We develop a dynamic theory of how stimuli are mapped onto discrete (choice) and continuous response scales. It proposes that the mapping from stimuli to the input to an evidence accumulation process is accomplished using multiple reference points or "anchors". Evidence is accumulated until a threshold amount for a particular response is obtained, with the relative balance of support for each anchor at that time determining the response. We tested this Multiple Anchored Accumulation Theory (MAAT) using the results of two experiments requiring discrete or continuous responses to line length and color stimuli. We manipulated the number of options for discrete responses, the number of different stimuli, and the similarity amongst them, and compared the outcomes to continuous response conditions. We show that MAAT accounts for several key phenomena: more accurate choices and more skewed response distributions near the ends of a response scale; a decrease in accuracy and response speed as the number of discrete choice options increases; and longer response times and lower accuracy when discrete responses were more similar to one another. Our empirical and modeling results suggest that discrete and continuous response tasks can share a common evidence representation, and that the decision process is sensitive to the perceived similarity among the response options.

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Hick’s law: Its limit is 3 bits

Cited by 13 publications

References 9 publications

Hick’s law for choice reaction time: A review

Hick’s law for choice reaction time: A review

Information Theoretic Models of HCI: A Comparison of the Hick-Hyman Law and Fitts' Law

A unified theory of discrete and continuous responding

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