A simple theory of psychophysical scaling is presented. It is based on the power law and a multiplicative error model that treats magnitude judgments as lognormal variates. Conventional techniques for estimating power-law exponents are reviewed along with a solution to the problem of estimating parameters of psychophysical relationships when both variables in the relationship are measured with error. This problem arises when validating ratio scales of opinion by matching sensory magnitudes to social stimuli and thereby producing psychophysical cross-modality matching functions. The regression problem is reconsidered in this context and a method for dealing with it is proposed. Much is said in this volume of the importance of S. S. Stevens' contributions to psychophysical measurement. The past two decades have indeed produced a proliferation of experimental findings based on the method of cross-modality matching that he popularized (Stevens, 1966). Although studies focused initially on the psychophysics of sensory function, with a major result being the revision of the psychophysical law, the new paradigms have also found fruitful application to the scaling of nonsensory variables such as seriousness of offenses, prestige of occupations, perceptions of national power and strength of opinion (Stevens, 1972). As applications have increased so have the methodological problems and issues (Stevens, 197Ia). More than ever we are aware of the need for standard treatment of such matters as parameter estimation, measurement error or judgment variability, the identification of sources of bias, and the measurement of bias. This paper outlines a simple theory of psychophysical scaling based on the power law and a multiplicative error model. Standard techniques for treating psychophysical data are reviewed. Most of them are familiar to psychophysicists but some of the results are derived from the proposed theory and are original solutions to some long standing problems in psychophysical scaling. Emphasis is placed on paradigms applicable to the scaling of social stimuli. The regression problem is reconsidered in this context and a method of dealing with it is proposed. Basic Psychophysical Theory It is assumed the presentation of a physical stimulus, <P, produces a perceptual response of variable magnitude, '1'" which is related to <P by the following psychophysical law :

Sensation and measurement.

http://vision.psychol.cam.ac.uk/jdmollon/papers/MollonKrauskopf1973.pdf

Reaction time as a measure of the temporal response properties of individual colour mechanisms

Foveal cone thresholds.

The duration-intensity relationship was investigated for a task in which triads of digits were to be identified. Critical durations (tc) of 200-350 msec. were found for 5 Ss. Under identical stimulus conditions tc for subjective brightness, determined by a matching method, was about 100 msec. for 2 of the Ss. It was concluded that tc varies as a function of perceptual task and that it does not represent the duration of an early "sensory" phase of the visual process. (21 ref.) (PsycINFO Database Record (c) 2012 APA, all rights reserved) Language: en

The time-intensity relation in visual perception as a function of observer's task.

Eighteen observers judged the apparent brightness of light flashes that varied in both duration and luminance. The median numerical estimations (made relative to a standard flash) confirmed three principles: the reciprocity between luminance and duration (Bloch's law), the enhancement of brightness at about 50 milliseconds (Broca-Sulzer effect), and the power-law relation between brightness and energy (Stevens's law).

http://science.sciencemag.org/content/sci/135/3497/42.full.pdf

Magnitude estimation of the brightness of brief foveal stimuli.

An experimental determination has been made of the effect of increasing size on the time interval over which the product of intensity and time is a constant Past research with white-light stimuli has shown It constancy to break down at progressively shorter exposure times as the diameter of a circular test field is increased up to 3 deg This experiment employed circular fields of red and blue-green monochromatic light centered in the peripheral retina 20 deg from the point of fixation Thresholds for durations from 313 to 1000 msec and areas of 343 min, 1 deg, 3 deg, and 8 deg were obtained by the method of constants The results for four subjects show that with both colors and all areas the product of threshold intensity and time is a constant for all exposure times up to 100 msec This is in direct contradiction to previous findings That these differences may depend on the spectral quality of the test light is discussed, as are the theoretical implications of the findings

Duration and size as determinants of peripheral retinal response.

An experimental determination was made of absolute visual thresholds in the human fovea. An apparatus permitting independent variation of area and exposure time, and having a fixation device that minimally affects the adaptation level of the region under investigation was used. Seven stimulus areas, ranging from 1 minute to 1 degree in diameter were presented to 4 subjects at durations of 1.1, 3.8, 10.0, and 48.0 milliseconds. The results show that all area-threshold functions depart from Ricco’s law. The functions which were obtained depart from linearity, while the degree of curvature varies among subjects. As exposure time is increased there is a regular related decrease in thresholds for all stimuli. This decrease in threshold is in good agreement with the Bunson-Roscoe law, which states that the product of time and intensity is a constant.

Beverly M. Hillmann

Papers

Duration and size as determinants of peripheral retinal response.

Relationship between stimulus size and threshold intensity in the fovea measured at four exposure times.