Empirical evaluation of a model of global psychophysical judgments: III. A form for the psychophysical function and intensity filtering

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Abstract

In part I, a concept of ratio estimation is defined and it is shown that if such estimates depend only upon the physical ratio of the signal to the reference signal, the psychophysical function must be a power function. Assuming the same exponents for each component, an invariance condition, equivalent to a sum of power functions, is studied empirically for binaural loudness. It is fully or partially sustained for 19 of 22 respondents. Since failures may be attributable to different exponents in the two ears, the ratio of the two exponents is estimated but that fails to explain the failures. Other possible explanations are suggested. In part II, an intensity filtering model is presented, accounting for the phenomenon where monaural loudness matches show a bias depending on the matching ear. We show (a) that the existence of such a bias does not alter the prior experimental results; and (b) assuming the power function, that five respondents attenuate the opposite ear and two enhance it.

Section snippets

The primitives and representation

Let the notation ( x , u ) denote the simultaneous presentation of the stimuli x in the left ear and u in the right one. More precisely, x denotes the physical intensity presented to the left ear less the threshold intensity for that ear, and u is the corresponding quantity for the right ear. Further, x and u are of the same frequency and are presented in phase.3

Ratio estimation

Ratio production is a fundamental primitive of our theory. But the dual process of ratio estimations for which the respondent is asked to state numerically the perceived ratio relation t = z / x between two experimenter-presented signals x and z is not part of the axiomatization. We remedy that theoretical lacuna.

Related to ratio estimation is the method of magnitude estimation, which is largely due to the influential contributions of Stevens, which are summarized in the posthumous book Stevens

Part II: intensity filtering

The topic of the present section is related to the earlier material primarily because power functions are assumed. The issue first arose in trying to understand a phenomenon that appeared in Experiment 1 of Steingrimsson and Luce (2005a). At that time we did not have a way to incorporate it into Luce, 2002, Luce, 2004 theoretical framework. We now believe we have such a description, which we call an intensity filtering model. In part I of the current paper, we explored the possibility of Ψ

Summary

Under the binaural loudness interpretation of the primitives, Steingrimsson and Luce, 2005a, Steingrimsson and Luce, 2005b tested and found adequate support for a number of behavioral axioms that together established the representations in (5) and (6). Here, we turned to the question of possible functional forms for the psychophysical functions ψ l and ψ r .

Under the assumption that ratio estimates are independent of the standard, (13), we arrived at the power function form (14) for ψ i . Under the

Acknowledgments

This research was supported in part by National Science Foundation grant SBR-9808057 to the University of California, Irvine. Additional financial support was provided by the School of Social Sciences and the Department of Cognitive Sciences at UCI. We are especially grateful to Dr. Bruce Berg for unfettered access to his laboratory, for technical assistance, and for help resolving a number of issues concerning psychoacoustical methodology. We thank the Center for Neural Science at New York

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    Nevertheless, Teghtsoonian (1973, p. 3) affirmed that “there is now considerable evidence that [the power relation] is not an artifact of pooling data over many observers but is evident in the behavior of individual observers”. More recently, Steingrimsson and Luce (2006) have shown that the power form may not be the best description for all individuals. Stevens limited his analysis to the average of the group and did not devote the same attention to measures of variability around this central tendency (see Piéron, 1963, p. 46).

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This article is based, in part, on the first author's Ph.D. dissertation (Steingrimsson, 2002).

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