Perception & Psychophysics

, Volume 35, Issue 6, pp 536–542 | Cite as

Perceived numerosity: A comparison of magnitude production, magnitude estimation, and discrimination judgments

  • Lester E. Krueger


In previous studies, modalities with a higher Weber fraction have tended to have a lower power-function exponent. Within a modality, however, the Weber fraction and power-function exponent for individual subjects were unrelated, and the present study largely confirms this finding for the numerosity dimension. More important than discriminability in the judgment of numerosity were cognitive factors. A single feedback trial considerably reduced intersubject variability on the magnitude-estimation exponent, although it failed to eliminate individual differences completely (precue and postcue exponents correlated signigicantly, r=+.50). Intrasubject variability, by contrast, seemingly did not involve the underlying exponent. As in previous studies, numerosity generally was underestimated and the power-function exponent was 1.08 for magnitude production and .80 for precue magnitude estimation. Contrary to previous results, however, males and females did not differ in exponent, perhaps because the present procedure allowed self-selection of individuals more interested in numerosity tasks.


  1. Auerbach, C. (1971). Interdependence of Stevens’ exponents and discriminability measures.Psychological Review,78, 556.CrossRefGoogle Scholar
  2. Baird, J. C. (1970). A cognitive theory of psychophysics: II. Fechnei’s law and Stevens’ law.Scandinavian Journal of Psychology,11, 89–102.CrossRefPubMedGoogle Scholar
  3. Baird, J. C., Romer, D., &Stein, T. (1970). Test of a cognitive theory of psychophysics: Size discrimination.Perceptual & Motor Skills,30, 495–501.Google Scholar
  4. Burgess, A., &Barlow, H. B. (1983). The precision of numerosity discrimination in arrays of random dots.Vision Research,23, 811–820.CrossRefPubMedGoogle Scholar
  5. Eisler, H. (1963). Magnitude scales, category scales, and Fechnerian integration.Psychological Review,70, 243–253.CrossRefGoogle Scholar
  6. Graf, V., Baird, J. C., &Glesman, G. (1974). An empirical test of two psychophysical models.Acta Psychologica,38, 59–72.CrossRefPubMedGoogle Scholar
  7. Heinemann, E. G. (1978). Discriminability and ratio scaling. In J. C. Armington, J. Krauskopf, & B. R. Wooten (Eds.),Visual psychophysics and physiology: A volume dedicated to Lomn Riggs pp. 157–166). New York: Academic Press.Google Scholar
  8. Indow, T., &Ida, M. (1977). Scaling of dot numerosity.Perception & Psychophysics,22, 265–276.CrossRefGoogle Scholar
  9. Kaufman, E. L., Lord, M. W., Reese, T. W., &Volkmann, J. (1949). The discrimination of visual number.American Journal of Psychology,62,498–525.CrossRefPubMedGoogle Scholar
  10. Krueger, L. E. (1972). Perceived numerosity.Perception & Psychophysics,11, 5–9.Google Scholar
  11. Krueger, L. E. (1982). Single judgments of numerosity.Perception & Psychophysics,31, 175–182.Google Scholar
  12. Minturn, A. L., &Reese, T. W. (1951). The effect of differential reinforcement on the discrimination of visual number.Journal of Psychology,31, 201–231.CrossRefGoogle Scholar
  13. Poulton, E. C. (1979). Models for biases in judging sensory magnitudes.Psychological Bulletin,86, 777–803.CrossRefPubMedGoogle Scholar
  14. Siegel, S. (1956).Nonparametric statistics for the behavioral sciences. New York: McGraw-Hill.Google Scholar
  15. Stevens, S. S. (1957). On the psychophysical law.Psychological Review,64, 153–181.CrossRefPubMedGoogle Scholar
  16. Stevens, S. S. (1966). Regression effect in psychophysical judgment.Perception & Psychophysics,1, 439–446.Google Scholar
  17. Stevens, S. S. (1971). Issues in psychophysical measurement.Psychological Review,78,426–450.CrossRefGoogle Scholar
  18. Teghtsoonian, M. (1965). The judgment of size.American Journal of Psychology,78, 392–402.CrossRefPubMedGoogle Scholar
  19. Teghtsoonian, M., &Teghtsoonian, R. (1983). Consistency of individual exponents in cross-modal matching.Perception & Psychophysics,33, 203–214.Google Scholar
  20. Teghtsoonian, R. (1971). On the exponents in Stevens’ law and the constant in Ekman’s law.Psychological Review,78, 71–80.CrossRefPubMedGoogle Scholar
  21. Teghtsoonian, R., &Teghtsoonian, M. (1978). Range and regression effects in magnitude scaling.Perception & Psychophysics,24, 305–314.Google Scholar
  22. van Oeffelen, M. P., &Vos, P. G. (1982). A probabilistic model for the discrimination of visual number.Perception & Psychophysics,32, 163–170.Google Scholar
  23. Wanschura, R. G., &Dawson, W. E. (1974). Regression effect and individual power functions over sessions.Journal of Experimental Psychology,102, 806–812.CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 1984

Authors and Affiliations

  • Lester E. Krueger
    • 1
  1. 1.Human Performance CenterOhio State UniversityColumbus

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