Inverse attribute functions and the proposed modifications of the power law

Dawson, William E.; Miller, Mark E.

doi:10.3758/bf03199744

Cited by 71 publications

(15 citation statements)

References 26 publications

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“…S. Stevens, 1959S. S. Stevens, , 1966Verrillo, 1974;Zwislocki, 1965Zwislocki, , 1974, whereas others suggest that numerical response bias plays a role (Dawson & Miller, 1978;Poulton, 1968). The fact that there were differences in the shapes of the functions between and within the data of the individual observers conflicts with physiological models that are based upon properties that should hold true for every individual and each condition.…”

Section: Discussionmentioning

confidence: 87%

The shape of the vibrotactile loudness function: The effect of stimulus repetition and skin-contactor coupling

Collins

Cholewiak

1994

Perception & Psychophysics

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In the psychophysical literature describing the relationships between physical and psychological magnitudes, as physical intensity increases, perceived intensity often grows much faster near threshold than at higher levels. In this laboratory, however, the loudness curve for sinusoidal vibrotactile stimuli was best fit by a single-limbed function rather than by the expected two-limbed function. In the present study, we measured the growth ofvibrotactile loudness of250-Hz sinusoidal stimuli by the method of absolute magnitude estimation to explore the source of the one-versus two-limbed discrepancy. The number of times that the stimulus was presented was varied, as well as whether the stimulator contacted the skin with constant force or constant penetration. Neither of these manipulations affected the shape ofthe loudness function consistently. Number of repetitions influenced the shapes of the magnitude estimation functions, but only for a few individuals. Skin-contactor coupling did not affect the shapes of the functions, although the absolute level (vibrotactile loudness) was consistently greater for constant indentation.

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Section: Discussionmentioning

confidence: 87%

The shape of the vibrotactile loudness function: The effect of stimulus repetition and skin-contactor coupling

Collins

Cholewiak

1994

Perception & Psychophysics

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“…To demonstrate how closely the power function with a low exponent (.05, .02, .01, or .001) mimics the logarithmic function, the measure constant, a, in the power function was adjusted to obtain the best fit 6 with the common logarithmic function, whose measure constant and absolute threshold value, Z o , were both set at 1.0 (i.e., S = log 7). An additive constant (fixed here, for convenience, at the value of a) was subtracted from the power function [i.e., S = a(I c ' k -1)], as is sometimes done to correct for curvature at the lower end of the power function (Dawson & Miller 1978). As a result, both functions predicted S = 0 at 7 -1.0, as shown in Figure 1.…”

Section: Power Functionmentioning

confidence: 99%

“…Marks (1974b) cited more fundamental problems with the category scale, such as its failure to show the Broca-Sulzer effect (Lewis 1965;Raab et al 1961): "It would appear, then, that rating procedures that limit the number of responses available to subjects may be constraining enough, at least in some instances, to camouflage important sensory phenomena" (p. 270). Another problem with the category scale is that it has no true zero point, although the need for an additive constant to remove curvature in the magnitude scale (Dawson & Miller 1978) leaves doubt as to whether that scale has any truer zero point. Finally, it should be noted that an uncorrected (for the scaling of number) magnitude scale may be preferable to a corrected one in most immediate practical applications.…”

Section: Number Use In Category Ratingsmentioning

confidence: 99%

Reconciling Fechner and Stevens: Toward a unified psychophysical law

1989

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How 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.

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“…Parameter values vary across stimulus types and experimental conditions (Marks and Stevens, 1968;Fagot, 1975;Eisler, 1976;Dawson and Miller, 1978;Allan, 1983) and one must consider a family μ i , in which the subscript (also in the parameters) denotes condition. Within a condition, subjective duration exceeds objective duration within the range of t for which μ i (t) > t whereas subjective duration is shorter than objective duration wherever μ i (t) < t. Figure 1 showed two psychophysical functions described by Equation (1).…”

Section: A Unified Model Of Performance Across Semi-objective Psychopmentioning

confidence: 99%

The Role of Parametric Assumptions in Adaptive Bayesian Estimation.

Alcalá-Quintana

Garcı́a-Pérez

2004

Psychological Methods

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Time perception is studied with subjective or semi-objective psychophysical methods. With subjective methods, observers provide quantitative estimates of duration and data depict the psychophysical function relating subjective duration to objective duration. With semi-objective methods, observers provide categorical or comparative judgments of duration and data depict the psychometric function relating the probability of a certain judgment to objective duration. Both approaches are used to study whether subjective and objective time run at the same pace or whether time flies or slows down under certain conditions. We analyze theoretical aspects affecting the interpretation of data gathered with the most widely used semi-objective methods, including single-presentation and paired-comparison methods. For this purpose, a formal model of psychophysical performance is used in which subjective duration is represented via a psychophysical function and the scalar property. This provides the timing component of the model, which is invariant across methods. A decisional component that varies across methods reflects how observers use subjective durations to make judgments and give the responses requested under each method. Application of the model shows that psychometric functions in single-presentation methods are uninterpretable because the various influences on observed performance are inextricably confounded in the data. In contrast, data gathered with paired-comparison methods permit separating out those influences. Prevalent approaches to fitting psychometric functions to data are also discussed and shown to be inconsistent with widely accepted principles of time perception, implicitly assuming instead that subjective time equals objective time and that observed differences across conditions do not reflect differences in perceived duration but criterion shifts. These analyses prompt evidence-based recommendations for best methodological practice in studies on time perception.

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Inverse attribute functions and the proposed modifications of the power law

Cited by 71 publications

References 26 publications

The shape of the vibrotactile loudness function: The effect of stimulus repetition and skin-contactor coupling

The shape of the vibrotactile loudness function: The effect of stimulus repetition and skin-contactor coupling

Reconciling Fechner and Stevens: Toward a unified psychophysical law

The Role of Parametric Assumptions in Adaptive Bayesian Estimation.

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