Skip to main content
SpringerLink
Log in

Psychophysical study of Numbers

V. Preferred state theory of matching functions

  • Published:
Psychological Research Aims and scope Submit manuscript

Summary

This paper describes an extension of Preferred State Theory (Baird, 1975) to deal with matching functions produced by such techniques as magnitude and category estimation. It is assumed by this theory that all stimulus attributes are transformed into perceptual states according to the operation of mathematical base systems. Intensities are matched across attributes in terms of the number of preferred states generated by each. The theory provides quantitative explanations for a variety of psychophysical effects, including the prothetic-metathetic distinction, the selective applicability of Fechner's and Stevens' laws, and the success of transitivity tests among exponents.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Attneave, F.: Perception and related areas. In: Psychology: A study of a science, Vol. 4 (Koch, S., Ed.). New York: McGraw Hill 1962

    Google Scholar 

  • Baird, J. C.: A cognitive theory of psychophysics. I. Information transmission, partitioning, and Weber's law. Scand. J. Psychol. 11, 35–46 (1970a)

    Google Scholar 

  • Baird, J. C.: A cognitive theory of psychophysics. II. Fechner's law and Stevens' law. Scand. J. Psychol. 11, 89–102 (1970b)

    Google Scholar 

  • Baird, J. C.: Psychophysical analysis of visual space. London: Pergamon 1970c

    Google Scholar 

  • Baird, J. C.: Psychophysical study of numbers: IV. Generalized preferred state theory. Psychol. Res. (1975)

  • Baird, J. C., Lewis, C., Romer, D.: Relative frequencies of numerical responses in ratio estimation. Perception and Psychophysics 8, 358–362 (1970)

    Google Scholar 

  • Baird, J. C., Noma E.: Psychophysical study of numbers: I. Generation of numerical responses. Psychol. Res. 37, 281–287 (1975)

    Google Scholar 

  • Baird, J. C., Stein, T.: When power functions fail: A theoretical explanation. Perceptual and Motor Skills 30, 415–425 (1970)

    Google Scholar 

  • Banks, W. P.: A new psychophysical ratio scaling technique: Random Production. Bull. Psychonomic Soc. 1, 273–275 (1973)

    Google Scholar 

  • Eisler, H.: A general differential equation in psychophysics. Scand. J. Psychol. 4, 265–272 (1963)

    Google Scholar 

  • Eisler, H., Montgomery, H.: On theoretical and realizable ideal conditions in psychophysics: Magnitude and category scales and their relation. Göteborg Pschological Reports. The University of Göteborg 2, No. 16 (1972)

  • Ekman, G.: Subjective power functions and the method of fractionation. Reports from the Psychological Laboratories. The University of Stockholm, No. 34 (1956)

  • Ekman, G.: Weber's law and related functions. J. Psychol. 47, 343–352 (1959)

    Google Scholar 

  • Ekman, G.: Is the power law a special case of Fechner's law? Perceptual and Motor Skills 19, 73 (1974)

    Google Scholar 

  • Ekman, G., Sjöberg, L.: Scaling. Annual Review of Psychology 16, 451–474 (1965)

    Google Scholar 

  • Engen, T., Levy, N.: The influence of standards on psychophysical judgments. Perceptual and Motor Skills 5, 193–197 (1955)

    Google Scholar 

  • Engen, T., Ross, B. M.: Effect of reference number of magnitude estimation. Perception and Psychophysics 1, 74–76 (1966)

    Google Scholar 

  • Fechner, G.: Elemente der Psychophysik, Vol. II. Leipzig: Breitkopf and Bartel 1907

    Google Scholar 

  • Freides, D., Phillips, P.: Power law fits to magnitude estimates of groups and individuals. Psychonomic Sci. 5, 367–368 (1966)

    Google Scholar 

  • Gibson, R.H., Tomko, D. L.: The relation between category and magnitude estimates of tactile intensity. Perception and Psychophysics. 12, 135–138 (1972)

    Google Scholar 

  • Graf, V., Baird, J. C., Glesman, G.: An empirical test of two psychophysical models. Acta psychol. 38, 59–72 (1974)

    Google Scholar 

  • Helm, C. E., Messick, S., Tucker, L. R.: Psychological models for relating discrimination and magnitude estimation scales. Psychol. Rev. 68, 167–177 (1961)

    Google Scholar 

  • Helson, H.: Adaptation-level theory. New York: Harper and Row 1964

    Google Scholar 

  • Künnapas, T.: Scales for subjective distance. Scand. J. Psychol. 1, 187–192 (1960)

    Google Scholar 

  • 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)

    Google Scholar 

  • Marks, L. E.: Stimulus range, number of categories, and form of the category scale. Amer, J. Psychol. 81, 467–479 (1968)

    Google Scholar 

  • Marks, L. E., Stevens, J. C.: The form of the psychophysical function near threshold. Perception and Psychophysics 4, 315–318 (1968)

    Google Scholar 

  • Mashhour, M., Hosman, J.: On the new psychophysical law. A validation study. Perception and Psychophysics 3, 367–375 (1968)

    Google Scholar 

  • 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

    Google Scholar 

  • McKay, D. M.: Psychophysics of perceived intensity: A theoretical basis for Fechner's and Stevens' laws. Science 139, 1212–1216 (1963)

    Google Scholar 

  • Noma, E., Baird, J. C.: Psychophysical study of numbers. II. Theoretical models of number generation. Psychol. Res. 38, 81–96 (1975)

    Google Scholar 

  • Poulton, E. C.: The new psychophysics: Six models for magnitude estimation. Psychol. Bull. 69, 1–19 (1968)

    Google Scholar 

  • Poulton, E. C.: Choice of first variables for single and repeated multiple estimates of loudness. J. exp. Psychol. 80, 249–253 (1969)

    Google Scholar 

  • Pradhan, P. L., Hoffman, P. J.: Effect of spacing and range of stimuli on magnitude estimation judgments. J. exp. Psychol. 66, 533–541 (1963)

    Google Scholar 

  • Stevens, S. S.: On the brightness of lights and the loudness of sounds. Science 118, 576 (1953) (Abstract)

    Google Scholar 

  • Stevens, S. S.: To honor Fechner and repeal his law. Science 133, 80–86 (1961)

    Google Scholar 

  • Stevens, S. S.: On the operation known as judgment. American Scientist 54, 385–401 (1966a)

    Google Scholar 

  • Stevens, S. S.: A metric for the social consensus. Science 151, 530–541 (1966b)

    Google Scholar 

  • Stevens, S. S.: Neural events and the psychophysical law. Science 170, 1043–1050 (1970)

    Google Scholar 

  • Stevens, S. S.: Issues in Psychophysical measurement. Psychol. Rev. 78, 426–450 (1971)

    Google Scholar 

  • Stevens, S. S., Galanter, E. H.: Ratio scales and category scales for a dozen perceptual continua. J. exp. Psychol. 54, 377–411 (1957)

    Google Scholar 

  • Teghtsoonian, R.: On the exponents in Stevens' law and the constant in Ekman's law. Psychol. Rev. 8, 71–80 (1971)

    Google Scholar 

  • Treisman, M.: Sensory scaling and the psychphysical law. Quart. J. exp. Psychol. 16, 11–22 (1964)

    Google Scholar 

  • Wandmacher, J.: Die Trennung von sensorischen und Urteilsprozessen bei der Größen- und Verhältnisschätzung. Doctoral dissertation, University of Hamburg (1970)

  • Ward, L. M.: Category judgments of loudnesses in the absence of an experimenter-induced identification function: Sequential effects and power function fit. J. exp. Psychol. 94, 179–184 (1972)

    Google Scholar 

  • Ward, L. M.: Repeated magnitude estimations with a variable standard: Sequential effects and other properties. Perception and Psychophysics 13, 193–200 (1973)

    Google Scholar 

  • Ward, L. M., Lockhead, G. R.: Response system processes in absolute judgment. Perception and Psychophysics 9, 73–78 (1971)

    Google Scholar 

  • Weissmann, W. M., Holligsworth, S. R., Baird, J. C.: Psychophysical study of numbers. III. Methodological applications. Psychol. Res. 38, 97–115 (1975)

    Google Scholar 

  • Wong, R.: Effect of the modulus on estimates of magnitude of linear extent. Amer. J. Psychol. 76, 511–521 (1963)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Psychology, Dartmouth College, 03755, Hanover, New Hampshire, USA

    John C. Baird

Authors
  1. John C. Baird
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This article is the last in a series. The ideas discussed here were first presented at the 1973 meetings of the Psychonomic Society. I am grateful to Charles Lewis, Elliot Noma, and Stephen Weissmann for their encouragement and advice on many aspects of the work.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baird, J.C. Psychophysical study of Numbers. Psychol. Res 38, 189–207 (1975). https://doi.org/10.1007/BF00308524

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00308524

Keywords

Search

Navigation