Empirical evaluation of a model of global psychophysical judgments: III. A form for the psychophysical function and intensity filtering
Section snippets
The primitives and representation
Let the notation 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 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
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 and .
Under the assumption that ratio estimates are independent of the standard, (13), we arrived at the power function form (14) for . 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
References (17)
- et al.
Evaluating a model of global psychophysical judgments: I. Behavioral properties of summations and productions
Journal of Mathematical Psychology
(2005) - et al.
Evaluating a model of global psychophysical judgments: II. Behavioral properties linking summations and productions
Journal of Mathematical Psychology
(2005) Lectures on functional equations and their applications
(1966)- et al.
Functional equations in the behavioral sciences
Mathematica Japonica
(2000) Ethical principles of psychologists and code of conduct
American Psychologist
(1992)Specification for audiometers (ANSI S3.6-1996)
(1996)- et al.
Magnitude of the standard, numerical value of the standard, and stimulus spacing in the estimation of loudness
Perceptual and Motor Skills
(1965) - et al.
An introduction to the bootstrap
(1993)
Cited by (27)
-
An adaptive infrared image segmentation method based on fusion SPCNN
2020, Signal Processing: Image Communication -
Subjective intensity: Behavioral laws, numerical representations, and behavioral predictions in Luce's model of global psychophysics
2016, Journal of Mathematical Psychology -
What are we estimating when we fit Stevens’ power law?
2016, Journal of Mathematical PsychologyCitation Excerpt :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).
-
The psychophysical function and separable model forms in joint magnitude estimation
2016, Journal of Mathematical Psychology -
Empirical properties of group preference aggregation methods employed in AHP: Theory and evidence
2014, European Journal of Operational Research -
Evaluating decision maker "type" under p-additive utility representations
2013, Journal of Mathematical Psychology
- 1
-
This article is based, in part, on the first author's Ph.D. dissertation (Steingrimsson, 2002).