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.

Fechner's Law: Where Does the Log Transform Come From?

2010 ◽  
Vol 23 (2) ◽  
pp. 155-171 ◽  
Author(s):  
Donald Laming
Keyword(s):  
General Theory ◽  
Signal Detection ◽  
Degrees Of Freedom ◽  
Weber’S Law ◽  
Sensory Discrimination ◽  
Weber's Law ◽  
Detection Model ◽  
Physical Magnitude ◽  
Equal Variance ◽  
Internal Sensation

AbstractThis paper looks at Fechner's law in the light of 150 years of subsequent study. In combination with the normal, equal variance, signal-detection model, Fechner's law provides a numerically accurate account of discriminations between two separate stimuli, essentially because the logarithmic transform delivers a model for Weber's law. But it cannot be taken to be a measure of internal sensation because an equally accurate account is provided by a χ2 model in which stimuli are scaled by their physical magnitude. The logarithmic transform of Fechner's law arises because, for the number of degrees of freedom typically required in the χ2 model, the logarithm of a χ2 variable is, to a good approximation, normal. This argument is set within a general theory of sensory discrimination.

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 The Series of a Four-node Motif can Provide Sensitive Detection over Arbitrary Range of Signal, thereby Explain Weber’s Law in Higher-Order Sensory Processes, and Compute Logarithm

2020 ◽  
Author(s):  
Dinkar Wadhwa
Keyword(s):  
Linear Model ◽  
Sensory System ◽  
Sound Intensity ◽  
Sensitive Detection ◽  
General Mechanism ◽  
Weber’S Law ◽  
Weber's Law ◽  
Cone Opsins ◽  
Sensory Processes ◽  
Bow Tie

AbstractWeber’s law states that the ratio of the smallest perceptual change in a signal and the background signal is constant. The law is observed across the perception of weight, light intensity, and sound intensity and pitch. Conventionally, two models of perception have been proposed to explain Weber’s law, namely the logarithmic and the linear model. Later, another formulation of Weber’s law was proposed which links it with exact adaptation. This paper argues in favour of the linear model, which requires the sensory system to generate linear signal-response relationship over several orders of magnitude. To this end, a four-node motif is constructed from first principles whose series provides linear relationship between signal and response over arbitrary range of signal. The motif also reproduces the neuronal data of numerosity detection study on monkey. The series of this motif provides a general mechanism for sensitive detection over arbitrary range of signal. The series also provides a general basis for a class of bow-tie architecture where the number of receptors is much lower than the range of signal and response. Besides numerosity processing, another example of this class of bow-tie architecture that the series of this motif is able to produce is absorption spectra of cone opsins of humans. Further, the series can compute logarithm over arbitrary range of signal.

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.

Sign in / Sign up

Export Citation Format

Share Document