Single-parameter Power Law Psychophysics of Auditory Numerosity and the Psychological Moment Hypothesis

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 trial) 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 single-parameter power law exponent for numerosity, which was found to be 0.80.