Skip to main content
Log in

Psychophysical study of numbers

I. Generation of numerical responses

Psychological Research Aims and scope Submit manuscript

Summary

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.

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

Access this article

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

Instant access to the full article PDF.

Institutional subscriptions

References

  • 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 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.: 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)

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

    Google Scholar 

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

    Google Scholar 

  • 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 

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

    Google Scholar 

  • Banks, W. P., Hill, D. K.: The apparent magnitude of number scaled by random production. J. exp. Psychol. Monogr. 102 (No. 2) (1974)

  • 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 

  • 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 

  • Eagleston, O. W., Lipford, E. J.: A study of number choices. J. genet. Psychol. 31, 129–133 (1944)

    Google Scholar 

  • Ekman, G.: Is the power law a special case of Fechner's law? Perceptual and Motor Skills 19, 730 (1964)

    Google Scholar 

  • Ekman, G., Hosman, B.: Note on subjective scales of number. Perceptual and Motor Skills 21, 101–102 (1965)

    Google Scholar 

  • 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 

  • Engen, T., Ross, B. M.: Effect of reference number on magnitude estimation. Percept. Psychophys. 1, 74–76 (1966)

    Google Scholar 

  • Fechner, G. E.: Elemente der Psychophysik, Bd. II. Leipzig: Breitkopf und Hartel 1907

    Google Scholar 

  • Galton, F.: Visualized numerals. J. anthropol. Inst. 10, 85–97 (1880)

    Google Scholar 

  • Heywood, S.: The popular number seven or number preference. Perceptual and Motor Skills 34, 357–358 (1972)

    Google Scholar 

  • McGill, W.: The slope of the loudness function: A puzzle. In: Gulliksen, H., Messick, S. (Eds.): Psychological scaling: Theory and applications. New York: Wiley 1960

    Google Scholar 

  • Rosner, B. S.: The power law and subjective scales of number. Perceptual and Motor Skills 21, 42 (1965)

    Google Scholar 

  • Ross, B. M., Engen, T.: Effects of round number preferences in a guessing task. J. exp. Psychol. 58, 462–468 (1959)

    Google Scholar 

  • Ross, S., Kohl, D. M.: Perceptual factors in number choices. J. genet. Psychol. 39, 39–47 (1948)

    Google Scholar 

  • Rule, S. J.: Equal discriminability scale of number. J. exp. Psychol. 79, 35–38 (1969)

    Google Scholar 

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

    Google Scholar 

  • Teghtsoonian, M., Teghtsoonian, R.: How repeatable are Stevens' power law exponents for individual subjects? Percept. Psychophys. 10, 147–149 (1971)

    Google Scholar 

  • Teghtsoonian, R.: On the exponents in Stevens' law and the constant in Ekman's law. Psychol. Rev. 78, 71–80 (1971)

    Google Scholar 

  • Wagenaar, W. A.: Generation of random sequences by human subjects.: A critical survey of the literature. Psychol. Bull. 77, 65–72 (1972)

    Google Scholar 

  • Winick, C.: Preference for individual digits. J. genet. Psychol. 67, 271–281 (1962)

    Google Scholar 

  • Wong, R.: Effect of the modulus on estimates of magnitude of linear extent. Amer. J. Psychol. 76, 511–512 (1963)

    Google Scholar 

  • Yule, G. U.: On reading a scale. J. roy. statist. Soc. 90, 570 (1927)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

We thank Charles Lewis of the University of Illinois for advice on statistical problems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Baird, J.C., Noma, E. Psychophysical study of numbers. Psychol. Res 37, 281–297 (1975). https://doi.org/10.1007/BF00309723

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00309723

Keywords

Navigation