Psychological Research

, Volume 37, Issue 4, pp 281–297 | Cite as

Psychophysical study of numbers

I. Generation of numerical responses
  • John C. Baird
  • Elliot Noma


Two experiments were conducted to study the number biases of subjects in situations not involving the usual psychophysical stimuli. In Exp. I subjects were asked to generate numbers (within boundary conditions) they thought other people would produce under the same conditions. In Exp. II only a single lower boundary (e.g., 1,10 or 100) was employed and subjects generated a set of numbers larger than the boundary. Results suggested that definite number biases exist. Multiples of 1, 10, 100 and to a lesser extent 5, 50 and 500 dominate and are appropriate to the log cycle. That is, multiples of 1 occur most often in the cycle 1–10, multiples of 10 in the cycle 10–100, etc. The implications of these results are noted for several psychophysical theories.


Boundary Condition Lower Boundary Psychophysical Study Definite Number Psychophysical Theory 
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  1. Attneave, F.: Perception and related areas. In: Koch, S. (Ed.): Psychology: A study of a science, Vol. 4, pp. 619–659. New York: McGraw-Hill 1962Google Scholar
  2. 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
  3. Baird, J. C.: A cognitive theory of psychophysics. II. Fechner's law and Stevens' law. Scand. J. Psychol. 11, 89–102 (1970b)Google Scholar
  4. Baird, J. C.: Information processing in alternative visual spaces. Chapter in: Baird, J. C. (Ed.): Human space perception: Proceedings of the Dartmouth conference. Psychonomic Monogr. Suppl. 3, (Whole No. 13) (1970c)Google Scholar
  5. Baird, J. C.: Psychophysical analysis of visual space. London: Pergamon 1970dGoogle Scholar
  6. Baird, J. C., Lewis, C., Romer, D.: Relative frequencies of numerical responses in ratio estimation. Percept. Psychophys. 8, 358–362 (1970)Google Scholar
  7. Baird, J. C., Kreindler, M., Jones, K.: Generation of multiple ratio scales with a fixed stimulus attribute. Percept. Psychophys. 9, 399–403 (1971)Google Scholar
  8. Banks, W. P.: A new psychophysical ratio scaling technique: Random production. Bull. Psychonom. Soc. 1, 273–275 (1973)Google Scholar
  9. Banks, W. P., Hill, D. K.: The apparent magnitude of number scaled by random production. J. exp. Psychol. Monogr. 102 (No. 2) (1974)Google Scholar
  10. Curtis, D. W.: Magnitude estimations and category judgments of brightness and brightness intervals: A two-stage interpretation. J. exp. Psychol. 83, 201–208 (1970)Google Scholar
  11. Curtis, D. W., Attneave, F., Harrington, T. L.: A test of a two-stage model of magnitude judgment. Percept. Psychophys. 3, 25–31 (1968)Google Scholar
  12. Eagleston, O. W., Lipford, E. J.: A study of number choices. J. genet. Psychol. 31, 129–133 (1944)Google Scholar
  13. Ekman, G.: Is the power law a special case of Fechner's law? Perceptual and Motor Skills 19, 730 (1964)Google Scholar
  14. Ekman, G., Hosman, B.: Note on subjective scales of number. Perceptual and Motor Skills 21, 101–102 (1965)Google Scholar
  15. Ekman, G., Hosman, B., Lindman, R., Ljungberg, L., Åkesson, C. A.: Interindividual differences in scaling performance. Perceptual and Motor Skills 26, 815–823 (1968)Google Scholar
  16. Engen, T., Ross, B. M.: Effect of reference number on magnitude estimation. Percept. Psychophys. 1, 74–76 (1966)Google Scholar
  17. Fechner, G. E.: Elemente der Psychophysik, Bd. II. Leipzig: Breitkopf und Hartel 1907Google Scholar
  18. Galton, F.: Visualized numerals. J. anthropol. Inst. 10, 85–97 (1880)Google Scholar
  19. Heywood, S.: The popular number seven or number preference. Perceptual and Motor Skills 34, 357–358 (1972)Google Scholar
  20. McGill, W.: The slope of the loudness function: A puzzle. In: Gulliksen, H., Messick, S. (Eds.): Psychological scaling: Theory and applications. New York: Wiley 1960Google Scholar
  21. Rosner, B. S.: The power law and subjective scales of number. Perceptual and Motor Skills 21, 42 (1965)Google Scholar
  22. Ross, B. M., Engen, T.: Effects of round number preferences in a guessing task. J. exp. Psychol. 58, 462–468 (1959)Google Scholar
  23. Ross, S., Kohl, D. M.: Perceptual factors in number choices. J. genet. Psychol. 39, 39–47 (1948)Google Scholar
  24. Rule, S. J.: Equal discriminability scale of number. J. exp. Psychol. 79, 35–38 (1969)Google Scholar
  25. Stevens, S. S.: On the operation known as judgment. Amer. Scientist 54, 385–401 (1966)Google Scholar
  26. Teghtsoonian, M., Teghtsoonian, R.: How repeatable are Stevens' power law exponents for individual subjects? Percept. Psychophys. 10, 147–149 (1971)Google Scholar
  27. Teghtsoonian, R.: On the exponents in Stevens' law and the constant in Ekman's law. Psychol. Rev. 78, 71–80 (1971)Google Scholar
  28. Wagenaar, W. A.: Generation of random sequences by human subjects.: A critical survey of the literature. Psychol. Bull. 77, 65–72 (1972)Google Scholar
  29. Winick, C.: Preference for individual digits. J. genet. Psychol. 67, 271–281 (1962)Google Scholar
  30. Wong, R.: Effect of the modulus on estimates of magnitude of linear extent. Amer. J. Psychol. 76, 511–512 (1963)Google Scholar
  31. Yule, G. U.: On reading a scale. J. roy. statist. Soc. 90, 570 (1927)Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • John C. Baird
    • 1
  • Elliot Noma
    • 1
  1. 1.Dartmouth CollegeHanover

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