Hick's Law Research Articles

Formation of requirements for the interface of university websites based on accessibility and usability standards

The subject of the research is the methods of building the user interface of university websites based on the intended purpose, the needs of the user audience and user limitations, including sensory-motor and cognitive-psychological limitations. As a starting point for the study of the target audience and compliance with accessibility standards, an analysis of eight university websites is carried out, based on data from open sources. The main violations that prevent the use of the University's website to varying degrees are considered, as well as the most well-known and often used approaches in interface design and design that make interfaces more convenient without overloading the user's short-term memory and without causing premature fatigue. As a result of the research, the basic requirements for the design of the interface of the university's website are formed. According to the main conclusion of this study, in order to adapt the University's website to the limitations of users' capabilities, it is necessary to follow the main standards of usability and accessibility considered, such as GOST R 52872-2019, WCAG 2.1 and GOST R ISO 9241-20-2014, and also take into account the peculiarities of legislation that affect the formation of sections of the site and its accessibility for people with disabilities. It is necessary to adhere to such principles of interface organization and information presentation as: Hick's Law, Gestalt Principles, Miller's Law, Jacob's Law and Heuristics. A special contribution of the author to the research of the topic is the analysis of the verification of eight sites of Russian universities for compliance with accessibility standards. This analysis showed that even the visually impaired versions of the sites reviewed do not meet accessibility standards, which makes it difficult for people with disabilities to access information and emphasizes the importance of the study. The novelty of the research lies in the formation of the basic requirements for the user interface of university websites. The results of the study can be further used in the construction of such information systems.

Efficiency of a Visual Search Explained by the Small-World Features of a Gaze Position Network

A visual search is implemented when the eye moves to find a target symbol amongst many other symbols (distractors). The efficiency of a visual search is described by Hick's law, which shows that the search time increases logarithmically as the number of symbols increases. In this paper, the efficiency of visual search was analyzed from the perspective of the network features of a conceptual ‘unobservable’ gaze position network superimposed on a monitor screen filled with many symbols (search array board). We assume that the gaze position does not move freely around the search array board, but rather moves in a way restricted to the unobservable gaze position network. First, we statistically verified that the artificial gaze position network designed from the data of visual search experiments have small-world features, and depends on the ratio of the saccades. Second, by implementing gaze step simulations on such small-world networks, we statistically verified that the simulation search times were close to those obtained from the experiments and also to the minimum search times. Thus, this study suggests that an efficient visual search can be explained by a small-world architecture hidden in the unobservable gaze position network and thus has to be artificially designed.

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

Robust parallel decision-making in neural circuits with nonlinear inhibition

An elemental computation in the brain is to identify the best in a set of options and report its value. It is required for inference, decision-making, optimization, action selection, consensus, and foraging. Neural computing is considered powerful because of its parallelism; however, it is unclear whether neurons can perform this max-finding operation in a way that improves upon the prohibitively slow optimal serial max-finding computation (which takes [Formula: see text] time for N noisy candidate options) by a factor of N, the benchmark for parallel computation. Biologically plausible architectures for this task are winner-take-all (WTA) networks, where individual neurons inhibit each other so only those with the largest input remain active. We show that conventional WTA networks fail the parallelism benchmark and, worse, in the presence of noise, altogether fail to produce a winner when N is large. We introduce the nWTA network, in which neurons are equipped with a second nonlinearity that prevents weakly active neurons from contributing inhibition. Without parameter fine-tuning or rescaling as N varies, the nWTA network achieves the parallelism benchmark. The network reproduces experimentally observed phenomena like Hick's law without needing an additional readout stage or adaptive N-dependent thresholds. Our work bridges scales by linking cellular nonlinearities to circuit-level decision-making, establishes that distributed computation saturating the parallelism benchmark is possible in networks of noisy, finite-memory neurons, and shows that Hick's law may be a symptom of near-optimal parallel decision-making with noisy input.

Accumulating advantages: A new conceptualization of rapid multiple choice.

Independent racing evidence-accumulator models have proven fruitful in advancing understanding of rapid decisions, mainly in the case of binary choice, where they can be relatively easily estimated and are known to account for a range of benchmark phenomena. Typically, such models assume a one-to-one mapping between accumulators and responses. We explore an alternative independent-race framework where more than one accumulator can be associated with each response, and where a response is triggered when a sufficient number of accumulators associated with that response reach their thresholds. Each accumulator is primarily driven by the difference in evidence supporting one versus another response (i.e., that response's "advantage"), with secondary inputs corresponding to the total evidence for both responses and a constant term. We use Brown and Heathcote's (2008) linear ballistic accumulator (LBA) to instantiate the framework in a mathematically tractable measurement model (i.e., a model whose parameters can be successfully recovered from data). We show this "advantage LBA" model provides a detailed quantitative account of a variety of benchmark binary and multiple choice phenomena that traditional independent accumulator models struggle with; in binary choice the effects of additive versus multiplicative changes to input values, and in multiple choice the effects of manipulations of the strength of lure (i.e., nontarget) stimuli and Hick's law. We conclude that the advantage LBA provides a tractable new avenue for understanding the dynamics of decisions among multiple choices. (PsycINFO Database Record (c) 2020 APA, all rights reserved).

Speed of saccadic responses and intelligence: An exponential-Gaussian analysis

Individual differences in the speed of making rapid eye movements (saccades) may have potential for exploring the link between neural conduction and cognitive abilities. Participants (N = 56) performed tasks devised to measure the speed at which humans started to move an eye towards a stimulus which appeared in peripheral vision (saccade) or in the opposite direction (anti-saccade). Cognitive abilities were measured using the Wide Range Intelligence Test, and ex-Gaussian parameters from the eye-movement tasks were correlated with these abilities. The findings showed that scores on the pro- and anti-saccade tests correlated substantially and that the anti-saccade condition led to consistently longer, more variable and more skewed responses. None of the parameters correlated significantly with the cognitive abilities assessed. The findings do not support the theory that nerve conduction velocity explains the correlation between reaction times and cognitive abilities. However, the findings do provide evidence of the existence of individual differences in saccadic eye-movements that can be captured by ex-Gaussian analysis of reaction time and also show that saccadic movements do not follow Hick's Law when task difficulty is manipulated.

Optimal policy for multi-alternative decisions.

Everyday decisions frequently require choosing among multiple alternatives. Yet the optimal policy for such decisions is unknown. Here we derive the normative policy for general multi-alternative decisions. This strategy requires evidence accumulation to nonlinear, time-dependent bounds that trigger choices. A geometric symmetry in those boundaries allows the optimal strategy to be implemented by a simple neural circuit involving normalization with fixed decision bounds and an urgency signal. The model captures several key features of the response of decision-making neurons as well as the increase in reaction time as a function of the number of alternatives, known as Hick's law. In addition, we show that in the presence of divisive normalization and internal variability, our model can account for several so-called 'irrational' behaviors, such as the similarity effect as well as the violation of both the independence of irrelevant alternatives principle and the regularity principle.

A model of the uncertainty effects in choice reaction time that includes a major contribution from effector selection.

Hick's law describes the relation between choice reaction time (RT) and the number of stimulus-response alternatives (NA). For over half a century, this uncertainty effect has been ascribed primarily to the time taken to map a stimulus to its associated response. Here, data from 2 experiments suggests that selection of the appropriate effector-the particular body part to make a response-also contributes substantially to the uncertainty effect. This insight is important both for our understanding of basic cognitive architecture and because many classic experiments studying stimulus-response mapping have confounded NA with the number of effectors. Our data also suggest that, when stimuli are spatial and linked to the responses in an intuitively simple layout, the time required for stimulus-response mapping depends minimally on the NA, independent of effector. Experiment 1 demonstrated that in order to account for the complex patterns of uncertainty effects observed when stimulus type (spatial vs. symbolic), response mode (typing, with multiple effectors vs. touching with a single, known effector), and participant population (skilled vs. novice typists) are all manipulated a model is required that includes effector selection, along with stimulus-response mapping, and a proper treatment of stimulus-response repetitions. Using spatial indicator stimuli that minimized the contributions of stimulus-response mapping, Experiment 2 compared 4 effector conditions-the factorial combination of 1 or 3 fingers on one or both hands. The results showed that the increase in the uncertainty effect associated with the number of effectors is negatively accelerated and possibly additive across the variation of hands and fingers. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

New Hick's law based reaction test App reveals “information processing speed” better identifies high falls risk older people than “simple reaction time”

The world is facing a major challenge on population aging and falls present a substantial health problem among the older population. The study is aimed to develop a reaction test App for assessing cognitive function related fall risks in older people. The developed App was tested on one hundred Korean women, consisting of twenty young healthy adults (age: 22.5 ± 0.6), forty community-dwelling older people with no history of falls (nonfallers; age: 72.5 ± 4.4) and forty matched older people with a history of falls (fallers; age: 71.8 ± 4.8). Simple reaction time and information processing speed of participants while performing the reaction test with the developed App were derived through a log-linear regression between the reaction time and number of equi-probable alternative choices based on Hick's law. Older people showed significantly longer simple reaction time and slower information processing speed than the young group. Even though there was no significant difference between older nonfallers and fallers on the simple reaction time (p = 0.54), the older fallers had significantly slower information processing speeds than older nonfallers (p < 0.001). Further, receiver operating characteristic analysis revealed excellent discriminative ability of information processing speed on classifying fallers and nonfallers, with sensitivity of 85% and specificity of 70%. These findings suggest slow information processing speed from the reaction test is an important risk factor for falling in older people. The developed reaction test App can be a convenient assessment tool for the older individuals and healthcare professionals to test cognitive function related falls risks.

Corrigendum.

CorrigendumCorrigendumPublished Online:27 Jan 2017https://doi.org/10.1152/jn.z9k-4005-corr.2016Original articleMoreSectionsPDF (48 KB)Download PDF ToolsExport citationAdd to favoritesGet permissionsTrack citations ShareShare onFacebookTwitterLinkedInWeChat Wong AL, Goldsmith J, Krakauer JW. A motor planning stage represents the shape of upcoming movement trajectories. J Neurophysiol 116: 296–305, 2016. First published April 20, 2016; doi: https://doi.org/10.1152/jn.01064.2015.A graphing error was discovered in Fig. 3A in which the heights of the point-to-point bars (reflecting reaction times) were incorrect. However, the point-to-point reaction time values plotted in Fig. 3B, as well as the numerical values reported in the text, are correct. As all statistics were conducted using the values reported in the text, this error does not affect the reported statistics or the conclusions of the paper.Fig. 3.Results from experiment 2. A: unlike point-to-point reaches generated in the context of curved movements (left bars), point-to-point RTs performed in isolation (right bars) were not modulated by the presence of a path cue [point-to-point with (PPlan) or without (PNoPlan) a path cue]. This finding is different from that noted in experiment 1, where an RT cost was observed for point-to-point movements. B: Hick's law curves for the Planning (blue) and No-Planning (green) conditions for different numbers of barrier configurations. Curve fits excluded the point-to-point movements performed in isolation (filled triangles). RTs of point-to-point movements generated in the context of curved reaches have been extracted for comparison (open triangles).Download figureDownload PowerPointThis article has no references to display. Download PDF Previous Back to Top FiguresReferencesRelatedInformation Related ArticlesA motor planning stage represents the shape of upcoming movement trajectories 01 Aug 2016Journal of Neurophysiology More from this issue > Volume 117Issue 1January 2017Pages 476-476 Copyright & PermissionsCopyright © 2017 the American Physiological Societyhttps://doi.org/10.1152/jn.z9k-4005-corr.2016PubMed28130389History Published online 27 January 2017 Published in print 1 January 2017 Metrics

Different (key)strokes for different folks: How standard and nonstandard typists balance Fitts' law and Hick's law.

Fine motor skills like typing involve a mapping problem that trades Fitts' law against Hick's law. Eight fingers have to be mapped onto 26 keys. Movement time increases with distance, so Fitts' law is optimized by recruiting more fingers. Choice difficulty increases with the number of alternatives, so Hick's law is optimized by recruiting fewer fingers. The effect of the number of alternatives decreases with consistent practice, so skilled typists achieve a balance between Fitts' law and Hick's law through learning. We tested this hypothesis by comparing standard typists who use the standard QWERTY mapping consistently with nonstandard typists who use fewer fingers less consistently. Typing speed and accuracy were lower for nonstandard typists, especially when visual guidance was reduced by removing the letters from the keys or covering the keyboard. Regression analyses showed that accommodation to Fitts' law (number of fingers) and Hick's law (consistency) predicted typing speed and accuracy. We measured the automaticity of typing in both groups, testing for hierarchical control in 3 tasks: word priming, which measures parallel activation of keystrokes, keyboard recall, which measures explicit knowledge of letter locations, and hand cuing, which measures explicit knowledge of which hand types which letter. Standard and nonstandard typists showed similar degrees of hierarchical control in all 3 tasks, suggesting that nonstandard typists type as automatically as standard typists, but their suboptimal balance between Fitts' law and Hick's law limits their ability to type quickly and accurately. (PsycINFO Database Record

Race to accumulate evidence for few and many saccade alternatives: an exception to speed-accuracy trade-off.

Hick's law states that increasing the number of response alternatives increases reaction time. Lawrence and colleagues report an exception to the law, whereby more alternatives lead to shorter saccadic reaction times (SRTs). Usher and McClelland (Psychol Rev 108(3):550-592. doi: 10.1037/0033-295X.108.3.550 , 2001) predict such an anti-Hick's effect when accuracy is not prioritized in a task, which should result in higher error rates with more response alternatives, and in turn to a shorter right tail of the SRT distribution. In the current study, we aim to replicate the original controversial findings and we compare them to these predictions by examining error rates and SRT distributions. Two experiments were conducted where participants made rapid eye movements to one of few or many alternatives. In Experiment 1, the saccade target was an onset and participants started either with few or many possible target locations and then alternated between conditions. An anti-Hick's effect emerged only when participants had started with a small set-size block. In Experiment 2, placeholders were displayed at the possible target locations and independent groups were used. A reliable anti-Hick's effect in SRTs was observed. However, results did not meet the stated predictions: anticipations and false direction errors were never more frequent when the set size was larger and SRT differences between the two set-size conditions were not more pronounced at the slower end of the distributions. In line with Lawrence and colleagues, we speculate that initial motor preparation, and the subsequent inhibition to counteract a premature response, may induce the anti-Hick's effect.

Probabilistic Decision Making with Spikes: From ISI Distributions to Behaviour via Information Gain.

Computational theories of decision making in the brain usually assume that sensory 'evidence' is accumulated supporting a number of hypotheses, and that the first accumulator to reach threshold triggers a decision in favour of its associated hypothesis. However, the evidence is often assumed to occur as a continuous process whose origins are somewhat abstract, with no direct link to the neural signals - action potentials or 'spikes' - that must ultimately form the substrate for decision making in the brain. Here we introduce a new variant of the well-known multi-hypothesis sequential probability ratio test (MSPRT) for decision making whose evidence observations consist of the basic unit of neural signalling - the inter-spike interval (ISI) - and which is based on a new form of the likelihood function. We dub this mechanism s-MSPRT and show its precise form for a range of realistic ISI distributions with positive support. In this way we show that, at the level of spikes, the refractory period may actually facilitate shorter decision times, and that the mechanism is robust against poor choice of the hypothesized data distribution. We show that s-MSPRT performance is related to the Kullback-Leibler divergence (KLD) or information gain between ISI distributions, through which we are able to link neural signalling to psychophysical observation at the behavioural level. Thus, we find the mean information needed for a decision is constant, thereby offering an account of Hick's law (relating decision time to the number of choices). Further, the mean decision time of s-MSPRT shows a power law dependence on the KLD offering an account of Piéron's law (relating reaction time to stimulus intensity). These results show the foundations for a research programme in which spike train analysis can be made the basis for predictions about behavior in multi-alternative choice tasks.

Using Mobile Devices for Motor-learning Laboratory Exercises

When teaching motor-learning concepts, laboratory experiments can be valuable tools for promoting learning. In certain circumstances, traditional laboratory exercises are often impractical due to facilities, time, or cost. Inexpensive or free applications (apps) that run on mobile devices can serve as useful alternatives. This article details three specific motor learning labs conducted by university students using mobile devices. Students used free apps to explore Hick's Law, Fitts's Law, and the distribution of practice (massed versus distributed). Final lab reports were equal in quality to past labs conducted without mobile devices, and the students reported generally favorable opinions of the experiences.

An optimal adjustment procedure to minimize experiment time in decisions with multiple alternatives

Decisions between multiple alternatives typically conform to Hick's Law: Mean response time increases log-linearly with the number of choice alternatives. We recently demonstrated context effects in Hick's Law, showing that patterns of response latency and choice accuracy were different for easy versus difficult blocks. The context effect explained previously observed discrepancies in error rate data and provided a new challenge for theoretical accounts of multialternative choice. In the present article, we propose a novel approach to modeling context effects that can be applied to any account that models the speed-accuracy trade-off. The core element of the approach is "optimality" in the way an experimental participant might define it: minimizing the total time spent in the experiment, without making too many errors. We show how this approach can be included in an existing Bayesian model of choice and highlight its ability to fit previous data as well as to predict novel empirical context effects. The model is shown to provide better quantitative fits than a more flexible heuristic account.

Context Effects in Multi-Alternative Decision Making: Empirical Data and a Bayesian Model

For decisions between many alternatives, the benchmark result is Hick's Law: that response time increases log-linearly with the number of choice alternatives. Even when Hick's Law is observed for response times, divergent results have been observed for error rates-sometimes error rates increase with the number of choice alternatives, and sometimes they are constant. We provide evidence from two experiments that error rates are mostly independent of the number of choice alternatives, unless context effects induce participants to trade speed for accuracy across conditions. Error rate data have previously been used to discriminate between competing theoretical accounts of Hick's Law, and our results question the validity of those conclusions. We show that a previously dismissed optimal observer model might provide a parsimonious account of both response time and error rate data. The model suggests that people approximate Bayesian inference in multi-alternative choice, except for some perceptual limitations.

Exploring attention-based explanations for some violations of Hick’s law for aimed movements

Choice reaction time generally increases linearly with the logarithm of the number of potential stimulus–response alternatives, a regularity known as Hick’s law. Two apparent violations of this generalization, which have been reported for aimed eye movements (Kveraga, Boucher, & Hughes, Experimental Brain Research, 146, 307–314, 2002), and arm movements (Wright, Marino, Belovsky, & Chubb, Experimental Brain Research, 179, 475–496, 2007), occurred when the indicator stimulus was an abrupt change at the location that was the target of the to-be-made movement. We report two experiments that examined and rejected the hypothesis that these abrupt-onset indicator stimuli triggered a shift in exogenous attention and that this led to unusually small uncertainty effects. Each experiment compared this indicator stimulus with a single alternative: Experiment 1 tested an indicator stimulus at all locations other than the target; Experiment 2 tested a central pointer to the target. Neither alternative led to an uncertainty effect for pointing responses that was of the size typically observed for other responses using the same stimuli.

An anti-Hick's effect in monkey and human saccade reaction times

In order to execute movements to targets in the environment, we must first select a target in which to move, generally from an array of alternatives. Hick's Law states that reaction time (RT) increases as the number of response alternatives increases. Violations of this law, however, generally in the form of the absence of a relationship between response alternatives and RT have been reported in the literature. K. Kveraga, L. Boucher, and H. C. Hughes (2002), for example, found that saccades to visual targets violate Hick's Law. To examine this violation further, we measured saccade RTs in monkeys and humans and found that saccade RTs actually decreased as the number of potential target locations increased. We hypothesize that this arises because subjects must actively inhibit premature saccades, and that the required inhibition increases as the certainty of a movement to a particular location increases. With increased inhibition, saccade onset is delayed, resulting in an anti-Hick's effect.

Neural Activity in the Frontal Eye Fields Modulated by the Number of Alternatives in Target Choice

Selection of identical responses may not use the same neural mechanisms when the number of alternatives (NA) for the selection changes, as suggested by Hick's law. For elucidating the choice mechanisms, frontal eye field (FEF) neurons were monitored during a color-to-location choice saccade task as the number of potential targets was varied. Visual responses to alternative targets decreased as NA increased, whereas perisaccade activities increased with NA. These modulations of FEF activities seem closely related to the choice process because the activity enhancements coincided with the timing of target selection, and the neural modulation was greater as NA increased, features expected of neural correlates for a choice process from the perspective of Hick's law. Our current observations suggest two novel notions of FEF neuronal behavior that have not been reported previously: (1) cells called "phasic visual" that do not discharge in the perisaccade interval in a delayed-saccade paradigm show such activity in a choice response task at the time of the saccade; and (2) the activity in FEF visuomotor cells display an inverse relationship between perisaccadic activity and the time of saccade triggering with higher levels of activity leading to longer saccade reaction times. These findings support the area's involvement in sensory-motor translation for target selection through coactivation and competitive interaction of neural populations that code for alternative action sets.

Behavioral properties of saccades generated as a choice response

The behavior characterizing choice response decision-making was studied in monkeys to provide background information for ongoing neurophysiological studies of the neural mechanisms underlying saccadic choice decisions. Animals were trained to associate a specific color from a set of colored visual stimuli with a specific spatial location. The visual stimuli (colored disks) appeared briefly at equal eccentricity from a central fixation position and then were masked by gray disks. The correct target association was subsequently cued by the appearance of a colored stimulus at the fixation point. The animal indicated its choice by saccading to the remembered location of the eccentric stimulus, which had matched the color of the cue. The number of alternative associations (NA) varied from 1 to 4 and remained fixed within a block of trials. After the training period, performance (percent correct responses) declined modestly as NA increased (on average 96, 93 or 84% correct for 1, 2 or 4 NA, respectively). Response latency increased logarithmically as a function of NA, thus obeying Hick's law. The spatial extent of the learned association between color and location was investigated by rotating the array of colored stimuli that had remained fixed during the learning phase to various different angles. Error rates in choice saccades increased gradually as a function of the amount of rotation. The learned association biased the direction of the saccadic response toward the quadrant associated with the cue, but saccade direction was always toward one of the actual visual stimuli. This suggests that the learned associations between stimuli and responses were not spatially exact, but instead the association between color and location was distributed with declining strength from the trained locations. These results demonstrate that the saccade system in monkeys also displays the characteristic dependence on NA in choice response latencies, while more basic features of the eye movements are invariant from those in other tasks. The findings also provide behavioral evidence that spatially distributed regions are established for the sensory-to-motor associations during training which are later utilized for choice decisions.