Single-parameter power law psychophysics of auditory numerosity and the psychological moment hypothesis

Abstract

In the present study, numerosity estimation was investigated. A two-parameter Stevens power law analysis was performed on a total of 944 subjects in six experiments. Two pulse ranges (2-17 or 17-253 pulses) and six pulse rates (either constant or randomly varied within trial blocks) were used, variously, in an unsuccessful attempt to find evidence for a psychological moment, under the supposition that the exponent (or, possibly, the measure constant) would become smaller as increasing numbers of pulses fell within the interval determined by each psychological moment. A single-parameter reanalysis of these six experiments under the initial value condition that a (standard) stimulus of one pulse be assigned a theoretical response (modulus) of one yielded single-parameter equations whose exponents were reliably less varied than those for conventional two-parameter equations in Experiments 1-4 (with randomly varying pulse rates from trial to triaD but not less varied in Experiments 5 and 6 (in which pulse rates were constant within trial blocks). It was concluded that the variable pulse rate condition, with its reduced exponent variability and presumed reduced temporal confounding, provides a more valid estimate of the singleparameter power law exponent for numerosity, which was found to be 0.80.Although we are intellectually aware that apparently continuous movie scenes are discontinuous, and that the visual field for each eye includes a sizable (but usually unnoticed) blind spot, the impression of visual continuity dominates our perception to the extent that such intellectual awareness does not disrupt the illusion. Presumably contributing in part to the illusion are insensitivity (in the case ofthe blind spot imaged onto an optic disk devoid ofphotoreceptor cells) and informational overload, wherein variations in sensory input occur at a rate exceeding the~en sory or perceptual capabilities of the sensory system (in the case of the apparently continuous movie). Stroud (1955) has suggested a perceptual moment hypothesis, which, although it is not specific with respect to the anatomical locus , represents an attempt to account for apparent informational limits in a variety of contexts, by means of the supposition that we can differentiate in psychological time repetitive physical events that we see or hear, provided that they are in separate psychological moments of time. This psychological (perceptual) moment corresponds to a typical duration ofapproximately 0.1 sec, but it may range from 0.05 to 0.2 sec for various circumstances. An implication of this hypothesis is illustrated by Stroud (1955, pp. 189-191) with reference to some preliminary unpublished work of Cheatham and White, who investigated subjects' ability to count repeated flashes Thanks are extended to Nancy B. Robinson for general assistance and to two anonymous reviewers for their comments on the manuscript. Correspondence may be addressed to

Temporal Processing Asymmetries Between the Cerebral Hemispheres: Evidence and Implications

“…Raninen, Franssila, & Rova mo, 1991), temporal order judge ments (Rutschm ann, 1973;Ulrich, 1987), two-flash fusion (Boynton, 1972), the detection of simultaneity (Allan, 1975;Baron, 1971), duration discrimination (Kristofferson, 1977(Kristofferson, , 1980, m etacontrast (U ttal, 1971) and temporal num erosity (W hite, 1963). For the auditory modality, temporal resolution has been investigated for temporal order judgem ents (Corso, 1980 ;Hirsh & Sherrick, 1961), temporal num erosity (Cheatnam & W hite, 1954;Robinson, 1992), two-click fusion (Boynton , 1972) and duration discrimination (Rousseau, Poirier, & Lem yre, 1983).…”

Perceiving the numerosity of rapidly occurring auditory events in metrical and nonmetrical contexts

“…Garner (1951), too, concluded from a control experiment that randomization of IOIs made little difference. Other authors, however, have found that experimental design does matter, especially at very fast presentation rates (John, 1972;Robinson, 1992). The training of participants also plays a role.…”

“…Interestingly, they obtained a similar estimate of subjective rate for auditory and visual stimuli (Cheatham & White, 1952;Forsyth & Chapanis, 1958;White, 1963;White & Cheatham, 1959;White, Cheatham, & Armington, 1953), and Cheatham and White (1954) thought that this amodal limit was related to the alpha rhythm of brain waves. However, John (1972) expressed reservations about the constancy of subjective rate in view of the effect of experimental design factors, and both he and others (Pollack, 1968;Robinson, 1992) have pointed out that there is an inevitable confound between numerosity perception and perception of sequence duration, especially at fast rates at which numerosity can only be estimated. Perhaps as a consequence of this realization, there has been little recent research on auditory numerosity perception.…”

Analyzing coefficients of psychophysical power functions

“…A number of researchers have examined the relation between the coefficient (or its logarithm) and the exponent for different experimental conditions or for individual subjects (e.g., Baird, Kreindler, & Jones, 1971;Gescheider & Hughson, 1991;Kowal, 1987;Robinson, 1992;Stevens, 1974), and most have found the coefficient to be negatively related to the exponent. From the point of view of the coefficient as an indication of the size of the response, the negative relation would suggest that subjects or experimental conditions that produce greater responses tend to yield lower exponents.…”

“…Rule, Department of Psychology, University of Alberta, Edmonton, AB, Canada, T6G 2E9. tin, 1983;Gescheider & Hughson, 1991;Kowal, 1987;Robinson, 1992). Some of these studies were designed to show that the unit of subjects' responses is stable with respect to changes in experimental procedure or with the same experimental procedure on different occasions.…”