scholarly journals Weber’s law is the result of exact temporal accumulation of evidence

2018 ◽  
Author(s):  
Jose L. Pardo-Vazquez ◽  
Juan Castiñeiras ◽  
Mafalda Valente ◽  
Tiago Costa ◽  
Alfonso Renart
Keyword(s):  
Reaction Time ◽  
Broad Class ◽  
Sequential Sampling ◽  
Behavioral Effect ◽  
Just Noticeable Difference ◽  
Weber’S Law ◽  
Discrimination Accuracy ◽  
Weber's Law ◽  
Evidence Accumulation ◽  
Hard Limit

AbstractWeber’s law states that the discriminability between two stimulus intensities depends only on their ratio. Despite its status as the cornerstone of psychophysics, the mecha-nisms underlying Weber’s law are still debated, as no principled way exists to choose between its many proposed alternative explanations. We studied this problem training rats to discriminate the lateralization of sounds of different overall level. We found that the rats’ discrimination accuracy in this task is level-invariant, consistent with Weber’s law. Surprisingly, the shape of the reaction time distributions is also level-invariant, implying that the only behavioral effect of changes in the overall level of the sounds is a uniform scaling of time. Furthermore, we demonstrate that Weber’s law breaks down if the stimulus duration is capped at values shorter than the typical reaction time. Together, these facts suggest that Weber’s law is associated to a process of bounded evidence accumulation. Consistent with this hypothesis, we show that, among a broad class of sequential sampling models, the only robust mechanism consistent with reaction time scale-invariance is based on perfect accumulation of evidence up to a constant bound, Poisson-like statistics, and a power-law encoding of stimulus intensity. Fits of a minimal diffusion model with these characteristics describe the rats performance and reaction time distributions with virtually no error. Various manipulations of motivation were unable to alter the rats’ psychometric function, demonstrating the stability of the just-noticeable-difference and suggesting that, at least under some conditions, the bound for evidence accumulation can set a hard limit on discrimination accuracy. Our results establish the mechanistic foundation of the process of intensity discrimination and clarify the factors that limit the precision of sensory systems.

scholarly journals A common mechanism underlies changes of mind about decisions and confidence

eLife ◽  
2016 ◽  
Vol 5 ◽  
Author(s):  
Ronald van den Berg ◽  
Kavitha Anandalingam ◽  
Ariel Zylberberg ◽  
Roozbeh Kiani ◽  
Michael N Shadlen ◽  
...  
Keyword(s):  
Reaction Time ◽  
Decision Process ◽  
Sequential Sampling ◽  
Common Mechanism ◽  
Perceptual Decision ◽  
Evidence Accumulation ◽  
Simple Processing ◽  
Degree Of Confidence ◽  
Initial Choice ◽  
Speed And Accuracy

Decisions are accompanied by a degree of confidence that a selected option is correct. A sequential sampling framework explains the speed and accuracy of decisions and extends naturally to the confidence that the decision rendered is likely to be correct. However, discrepancies between confidence and accuracy suggest that confidence might be supported by mechanisms dissociated from the decision process. Here we show that this discrepancy can arise naturally because of simple processing delays. When participants were asked to report choice and confidence simultaneously, their confidence, reaction time and a perceptual decision about motion were explained by bounded evidence accumulation. However, we also observed revisions of the initial choice and/or confidence. These changes of mind were explained by a continuation of the mechanism that led to the initial choice. Our findings extend the sequential sampling framework to vacillation about confidence and invites caution in interpreting dissociations between confidence and accuracy.

Reconciling Fechner and Stevens: Toward a unified psychophysical law

1989 ◽  
Vol 12 (2) ◽  
pp. 251-267 ◽  
Author(s):  
Lester E. Krueger
Keyword(s):  
Power Function ◽  
Category Scale ◽  
Just Noticeable Difference ◽  
Magnitude Scale ◽  
Weber’S Law ◽  
Weber's Law ◽  
Physical Magnitude ◽  
Subjective Magnitude ◽  
Number Magnitude ◽  
Sensory Processes

AbstractHow does subjective magnitude, S. increase as physical magnitude or intensity, I, increases? Direct ratings (magnitude scales; partition or category scales) can be fitted by the power function, S = aIb, in which S equals I raised to a power or exponent, b, and multiplied by a measure constant, a. The exponent is typically about twice as large for the magnitude scale (Stevens) as for the corresponding partition or category scale, but the higher exponent may be explained by the overly expansive way people use numbers in making magnitude estimations. The partition or category scale and the adjusted (for the use of number) magnitude scale for a given modality or condition generally agree with the neurelectric scale and the summated just noticeable difference (jnd) scale. A unified psychophysical law is proposed in which each jnd has the same subjective magnitude for a given modality or condition, subjective magnitude increases as approximately a power function of physical magnitude with the exponent ranging from near 0 to 1 (compressive function), and subjective magnitude depends primarily on peripheral sensory processes, that is, no nonlinear central transformations occur. An undue reliance on Weber's law blinded Fechner to the fact that the true psychophysical scale is approximately a power function. Rejecting Weber's law, which is not valid, means that we no longer have to choose between letting the summated jnd scale be a logarithmic function (Fechner's law) and introducing a nonlinear central transformation to make it into a power function (Brentano–Ekman-Teghtsoonian's law). Fechner and Stevens erred equally about the true psychophysical power function, whose exponent lies halfway between that of Fechner (an exponent approaching zero) and that of Stevens. To be reconciled, Fechnerians must give up the assumptions that Webers law is valid and that the jnd has the same subjective magnitude across modalities and conditions; Stevensians must give up the assumption that the unadjusted (for the use of number) magnitude scale is a direct measure of subjective magnitude.

scholarly journals Weber’s Law Applies to the Ants’ Visual Perception

2020 ◽  
Vol 11 (2) ◽  
pp. 36
Author(s):  
Marie-Claire Cammaerts ◽  
Roger Cammaerts
Keyword(s):  
Visual Perception ◽  
Operant Conditioning ◽  
Size Effects ◽  
Experimental Methodology ◽  
Just Noticeable Difference ◽  
Weber’S Law ◽  
Numerical Distance ◽  
Weber's Law

Non-numerical distance and size effects have been previously observed in the ant Myrmica sabuleti. As such effects can be theoretically in line with Weber’s law, we presumed that this law, until now examined in vertebrates, could also apply to ants. Using operant conditioning we trained then tested M. sabuleti workers faced with black circles having fixed diameters of 2, 3 and 4 mm against circles with diameters increasing by 0.5 mm until the ants perceived a difference between the smaller and the larger circles. This just noticeable difference occurred when the larger diameter reached 3.5, 5.5 and 7 mm respectively, what corresponded to a ratio larger/smaller surface of 3.06, 3.36 and 3.06. Owing to the degree of accuracy of the experimental methodology, this ratio is sufficiently constant for being consistent with Weber’s law.

Fechner's Elusive Parallel Law

2010 ◽  
Vol 23 (4) ◽  
pp. 335-348
Author(s):  
Helen Ross ◽  
Nicholas Wade
Keyword(s):  
Light Adaptation ◽  
Just Noticeable Difference ◽  
Differential Threshold ◽  
Adaptation Level ◽  
Weber’S Law ◽  
Weight Discrimination ◽  
Sensory Stimuli ◽  
Weber's Law ◽  
Perceived Values ◽  
Test Level

AbstractWeber's Law states that the differential threshold or just-noticeable-difference (jnd) is proportional to the physical intensity of the stimulus. Fechner built up his logarithmic law of sensation intensity from Weber's Law and the assumption that all jnds are subjectively equal. He thought it important that the Parallel Law should also hold. The Parallel Law states that, when perceived stimulus intensity is changed by something other than physical intensity (such as adaptation), Weber's Law continues to hold: discrimination should be unchanged provided the perceived values of the two stimuli change in the same ratio. Fechner claimed that weight discrimination was unaffected by weight adaptation; he was unsure about light adaptation; and he claimed that tactile length discrimination was unaffected by perceived changes caused by the bodily location of the stimulus. Modern research on adaptation for weights and other sensory stimuli shows that changes occur both in perceived intensity and in discrimination. Discrimination between stimuli is usually finest when the adaptation level is appropriate to the test level. There is insufficient evidence concerning the discrimination of tactile length and visual length when perceived length is changed. However, the Parallel Law may be untestable because of the difficulty of obtaining measures in the same experiment both for changes in discrimination and for the ratios of the perceived changes of the stimuli.

Does Motion Perception Follow Weber's Law?

Perception ◽  
1995 ◽  
Vol 24 (4) ◽  
pp. 363-372 ◽  
Author(s):  
Johannes M Zanker
Keyword(s):  
Motion Perception ◽  
Stimulus Intensity ◽  
Signal To Noise Ratio ◽  
Weber’S Law ◽  
Noise Levels ◽  
Signal To Noise ◽  
Weber's Law ◽  
The Absolute ◽  
Noise Ratio ◽  
Random Dot Patterns

The subjective strength of a percept often depends on the stimulus intensity in a nonlinear way. Such coding is often reflected by the observation that the just-noticeable difference between two stimulus intensities (JND) is proportional to the absolute stimulus intensity. This behaviour, which is usually referred to as Weber's Law, can be interpreted as a compressive nonlinearity extending the operating range of a sensory system. When the noise superimposed on a motion stimulus is increased along a logarithmic scale (in order to provide linear steps in subjective difference) in motion-coherency measurements, observers often report that the subjective differences between the various noise levels increase together with the absolute level. This observation could indicate a deviation from Weber's Law for variation of motion strength as obtained by changing the signal-to-noise ratio in random-dot kinematograms. Thus JNDs were measured for the superposition of uncorrelated random-dot patterns on static random-dot patterns and three types of motion stimuli realised as random-dot kinematograms, namely large-field and object ‘Fourier’ motion (all or a group of dots move coherently), ‘drift-balanced’ motion (a travelling region of static dots), and paradoxical ‘theta’ motion (the dots on the surface of an object move in opposite direction to the object itself). For all classes of stimuli, the JNDs when expressed as differences in signal-to-noise ratio turned out to increase with the signal-to-noise ratio, whereas the JNDs given as percentage of superimposed noise appear to be similar for all tested noise levels. Thus motion perception is in accordance with Weber's Law when the signal-to-noise ratio is regarded as stimulus intensity, which in turn appears to be coded in a nonlinear fashion. In general the Weber fractions are very large, indicating a poor differential sensitivity in signal-to-noise measurements.

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