Summary
The theory described in this paper is concerned with the perceptual and cognitive processes underlying psychophysical laws. The theory is a generalization of a model used to predict a subject's conception of the number continuum. It is assumed that all physical attributes (including numbers) undergo a perceptual transformation in terms of the operation of mathematical base systems. Different stimulus attributes are transformed by different bases, leading to transformed intensity values which are “preferred states.” Several new psychophysical equations are developed and compared with the laws of Fechner and Stevens.
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Attneave, F.: Perception and related areas. In: Psychology: A study of a science, Vol. 4 (Koch, S., Ed.). New York: McGraw-Hill 1962
Baird, J. C.: A cognitive theory of psychophysics. I. Information transmission, partitioning, and Weber's law. Scand. J. Psychol. 11, 35–46 (1970a)
Baird, J. C.: A cognitive theory of psychophysics. II. Fechner's law and Stevens' law. Scand. J. Psychol. 11, 89–102 (1970b)
Baird, J. C.: Information processing in alternative visual spaces. In: Human space perception: Proceedings of the Dartmouth conference (Baird, J. C., Ed.). Psychonomic Monogr. Suppl. 3, (Whole No. 45) (1970c)
Baird, J. C., Lewis, C., Romer, D.: Relative frequencies of numerical responses in ratio estimation. Perception and Psychophysics 8, 358–362 (1970)
Baird, J. C., Noma, E.: Psychophysical study of numbers. I. Generation of numerical responses. Psychol. Res. 37, 281–298 (1975)
Banks, W. P., Hill, D. K.: The apparent magnitude of number scaled by random production. J. exp. Psychol. Monogr. 102, (No. 2) (1974)
Eisler, H., Montgomery, H.: On theoretical and realizable ideal conditions in psychophysics: Magnitude and category scales and their relation. Göteborg Psychological Reports, The University of Göteborg 2, No. 16 (1972)
Ekman, G.: Is the power law a special case of Fechner's law? Perceptual and Motor Skills 19, 73 (1964)
Ekman, G., Sjöberg, L.: Scaling. Annual Review of Psychology 16, 451–474 (1965)
Engen, T.: Psychophysics. II. Scaling Methods. In: Woodworth and Schlosberg's experimental psychology (Kling, J. W., Riggs, L. A., Eds.). New York: Holt, Rinehart, & Winston, Inc. 1971
Fechner, G.: Elemente der psychophysik, Vol. II. Leipzig: Breitkopf and Hartel 1907
Freides, D., Phillips, P.: Power law fits to magnitude estimates of groups and individuals. Psychonomic Sci. 5, 367–368 (1966)
Guilford, J. P.: Psychometric methods. New York: McGraw-Hill 1954
Graf, V., Baird, J. C., Glesman, G.: An empirical test of two psychophysical models. Acta psychol. 38, 59–72 (1974)
Helson, H.: Adaptation-level theory. New York: Harper and Row 1964
Luce, R. D., Edwards, W.: The derivation of subjective scales from just-noticeable differences. Psychol. Rev. 65, 222–237 (1958)
Luce, R. D., Mo, S. S.: Magnitude estimation of heaviness and loudness by individual subjects: A test of a probabilistic response theory. British Journal of Mathematical and Statistical Psychology 18, 159–174 (1965)
Marks, L. E.: Stimulus range, number of categories, and form of the category scale. Amer. J. Psychol. 81, 467–479 (1968)
McGill, W.: The slope of the loudness function: A puzzle, p. 67–81. In: Psychological scaling: Theory and applications (Gulliksen, H., Messick, S., Eds.). New York: Wiley 1960
Noma, E., Baird, J. C.: Psychophysical study of numbers. II. Theoretical models of number generation. Psychol. Res. 38, 81–96 (1975)
Poulton, E. C.: The new psychophysics: Six models for magnitude estimation. Psychol. Bull. 69, 1–19 (1968)
Pradhan, P. L., Hoffman, P. J.: Effect of spacing and range of stimuli on magnitude estimation judgments. J. exp. Psychol. 66, 533–541 (1963)
Rule, S. J., Curtis, D. W.: Conjoint scaling of subjective number and weight. J. exp. Psychol. 97, 305–309 (1973)
Stevens, S. S.: On the operation known as judgment. American Scientist 54, 385–401 (1966)
Stevens, S. S.: Neural events and the psychophysical law. Science 170, 1043–1050 (1970)
Stevens, S. S.: Issues in psychophysical measurement. Psychol. Rev. 78, 426–450 (1971)
Stevens, S. S., Galanter, E. H.: Ratio scales and category scales for a dozen perceptual continua. J. exp. Psychol. 54, 377–411 (1957)
Teghtsoonian, R.: On the exponents in Stevens' law and the constant in Ekman's law. Psychol. Rev. 78, 71–80 (1971)
Treisman, M.: Sensory scaling and the psychophysical law. Quart. J. exp. Psychol. 16, 11–22 (1964)
Wandmacher, J.: Die Trennung von sensorischen und Urteilsprozessen bei der Grössen-und Verhältnisschätzung. Doctoral dissertation, University of Hamburg 1970
Warren, R. M.: Visual intensity judgments: An empirical rule and a theory. Psychol. Rev. 76, 16–30 (1969)
Weissmann, S. M., Hollingsworth, S. R., Baird, J. C. Psychophysical study of numbers. III. Methodological applications. Psychol. Res. 38, 97–115 (1975)
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This article is the fourth in a five-part series. The major ideas were developed while I was a visiting professor in the Psychologisches Institut, Universität Hamburg. I would like to thank Professor Kurt Pawlik of that institute for providing me with a convenient place to think. The theory was first presented at the 1973 meetings of the Psychonomic Society. I am grateful to Charles Lewis, Elliot Noma, and Stephen Weissmann for their criticism, encouragement and advice on many aspects of this work.
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Baird, J.C. Psychophysical study of numbers. Psychol. Res 38, 175–187 (1975). https://doi.org/10.1007/BF00308523
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DOI: https://doi.org/10.1007/BF00308523