Abstract

It is well known that, although psychophysical scaling produces good qualitative agreement between experiments, precise quantitative agreement between experimental results, such as that routinely achieved in physics or biology, is rarely or never attained. A particularly galling example of this is the fact that power function exponents for the same psychological continuum, measured in different laboratories but ostensibly using the same scaling method, magnitude estimation, can vary by a factor of three. Constrained scaling (CS), in which observers first learn a standardized meaning for a set of numerical responses relative to a standard sensory continuum and then make magnitude judgments of other sensations using the learned response scale, has produced excellent quantitative agreement between individual observers’ psychophysical functions. Theoretically it could do the same for across-laboratory comparisons, although this needs to be tested directly. We compared nine different experiments from four different laboratories as an example of the level of across experiment and across-laboratory agreement achievable using CS. In general, we found across experiment and across-laboratory agreement using CS to be significantly superior to that typically obtained with conventional magnitude estimation techniques, although some of its potential remains to be realized.

Highlights

  • One of the hallmarks of the success of the “scientific method” in achieving understanding of, and possibly some small bit of control over, the natural world is the precise replicability of the results of scientific experiments

  • In spite of many successes (e.g., Marks, 1974a), the second kind of measurement, including especially psychophysical scaling on which this paper focuses, has not yet achieved nearly the degree of reliability and precision required to demonstrate quantitative convergence across different laboratories and experimenters

  • A standard SoundBlaster sound card, a custom artificial ear, a Quest Technologies Model 2700 Precision Sound Level Meter, and Kenwood KPM-510 headphones were used in all experiments at University of British Columbia (UBC); a Tucker–Davis sound generator (RP2) and programmable attenuator (PA5), a Tucker–Davis artificial ear, and Sennheiser HD-200 headphones were used at McMaster; a SoundMax Integrated Digital Audio sound card from Analog Devices Inc., a Type 4153 Bruel & Kaer artificial ear, a Type 2260 Bruel & Kaer Modular Precision Sound Analyzer, and ATC-HA7USB Audio-Technica USB Digital Headphones were used at Tokyo Metropolitan; a VIA AC’97 generic motherboard sound card, a custom plaster-of-Paris artificial ear, a Sper Scientific Ltd

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Summary

Introduction

One of the hallmarks of the success of the “scientific method” in achieving understanding of, and possibly some small bit of control over, the natural world is the precise replicability of the results of scientific experiments. Imagine if the charge of the electron had a range of values that depended on who was doing the measurement experiment, or if the gas constant or the speed of light were not “constant” but depended on which investigator was writing about them This problem did occur early in the history of physics, for example in the measurement of temperature (e.g., Middleton, 1966), but it was solved by the adoption of consensual, standard, scales for the measurement of the basic physical variables (e.g., Ellis, 1966). If a theory, based on psychological, physiological and physical considerations, predicted that the exponent for loudness of a 1000 Hz tone should be 0.6 (e.g., Zwicker, 1982), that theory would be disconfirmed by the majority of scaling experiments reported to date, the average exponent over all such experiments is around 0.6 (Marks, 1974b)

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