Abstract
A bias model of relative judgment was used to derive a ratio estimation (RE) power function, and its effectiveness in providing estimates of exponents free of the effects of standards was evaluated. The RE bias model was compared with the simple RE power function that ignores bias. Results showed that when bias was not taken into account, estimates of exponents exhibited the usual effects of standards observed in previous research. However, the introduction of bias parameters into the RE power function virtually eliminated these effects. Exponents calculated from “equal-range segments” (e.g., low stimulus range vs. high stimulus range) judged by magnitude estimation (ME) were examined: the effects of equal-range segments on exponents were much stronger for ME than standards were for RE, using the bias model.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Adams, E. W., &Fagot, R. F. (1987). Monotonicity, convexity, and other qualitative psychophysical laws.Journal of Mathematical Psychology,31, 113–134.
Baird, J. C., &Noma, E. (1978).Fundamentals of scaling and psychophysics. New York: Wiley.
Beck, J., &Shaw, W. A. (1961). The scaling of pitch by the method of magnitude estimation.American Journal of Psychology,74, 242–251.
Beck, J., &Shaw, W. A. (1965). Magnitude of the standard, numerical value of the standard, and stimulus spacing in the estimation of loudness.Perceptual & Motor Skills,21, 151–156.
Bernyer, G. (1962). Étude sur la Validité d’une Échelle de Sensation d’effort Musculaire.Anné Psychologique,62, 1–15.
Birnbaum, M. H. (1982). Controversies in psychological measurement. In B. Wegener (Ed.),Social attitudes and psychophysical measurement (pp. 401–485). Hillsdale, NJ: Erlbaum.
Birnbaum, M. H., &Elmasian, R. (1977). Loudness “ratios” and “differences” involve the same psychophysical operation.Perception & Psychophysics,22, 383–391.
Cohen, J. (1973). Eta-squared and partial eta-squared in fixed factor ANOVA designs.Educational & Psychological Measurements,33, 107–112.
Cross, D. V. (1973). Sequential dependencies and regression in psychophysical judgments.Perception & Psychophysics,14, 547–552.
Cross, D. V. (1982). On Judgments Of Magnitude. In B. Wegener (Ed.),Social attitudes and psychophysical measurement (pp. 73–88). Hillsdale, NJ: Erlbaum.
Dodd, D. H., &Schultz, R. F., Jr. (1973). Computational procedures for estimating magnitude of effect for some analysis of variance designs.Psychological Bulletin,79, 391–395.
Ekman, G., Akesson, C. (1965). Saltness, sweetness, and preference: A study of qualitative relations in individual subjects.Scandinavian Journal of Psychology,6, 241–253.
Ekman, G., Hosman, B., Lindman, R., Ljungberg, L., &Akesson, C. (1968). Interindividual differences in scaling performance.Perceptual &. Motor Skills,26, 815–823.
Fagot, R. F. (1978). A theory of relative judgment.Perception & Psychophysics,24, 243–252.
Fagot, R. F. (1981). A theory of bidirectional judgments.Perception & Psychophysics,30, 181–193.
Fagot, R. F. (1982). Constructability and the power function for line judgments.Perception & Psychophysics,31, 392–394.
Hellman, R. P., &Zwislocki, J. J. (1961). Some factors affecting the estimation of loudness.Journal of the Acoustical Society of America,33, 687–694.
Jones, F. N., &Marcus, M. J. (1961). The subject effect in judgments of subjective magnitude.Journal of Experimental Psychology,61, 40–44.
Keppel, G. (1982).Design and analysis: A researchers handbook (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall.
Marks, L. E. (1974a). On scales of sensation: Prolegomena to any future psychophysics that will be able to come forth as science.Perception & Psychophysics,16, 358–376.
Marks, L. E. (1974b).Sensory processes: The new psychophysics. New York: Academic Press.
Marks, L. E., &Cain, W. S. (1972). Perception of intervals and magnitudes for three prothetic continua.Journal of Experimental Psychology,94, 6–17.
Marks, L. E., &Stevens, J. C. (1966). Individual brightness functions.Perception &. Psychophysics,1, 17–24.
Myers, J. L. (1979).Fundamentals of experimental design. Boston: Allyn & Bacon.
Parducci, A. (1982). Category ratings: Still more contextual effects! In B. Wegener (Ed.),Social attitudes and psychophysical measurement (pp. 89–105). Hillsdale, NJ: Erlbaum.
Poulton, E. C. (1968). The new psychophysics: Six models for magnitude estimation.Psychological Bulletin,69, 1–19.
Poulton, E. C. (1979). Models for biases in judging sensory magnitude.Psychological Bulletin,86, 777–803.
Rule, S. J. (1966). Subject differences in exponents of psychophysical power functions.Perceptual & Motor Skills,23, 1125–1126.
Rule, S. J., &Markley, R. P. (1971). Subject differences in cross modality matching.Perception & Psychophysics,9, 115–117.
Schneider, B., Parker, S., Farrell, G., &Kanow, G. (1976). The perceptual basis of loudness ratio judgments.Perception & Psychophysics,19, 309–320.
Schneider, B., Parker, S., &Stein, D. (1974). The measurement of loudness using direct comparisons of sensory intervals.Journal of Mathematical Psychology,11, 259–273
Shepard, R. N. (1981). Psychological relations and psychological scales. On the status of “direct” psychophysical measurement.Journal of Mathematical Psychology,24, 21–57.
Stevens, J. C., &Guirao, M. (1964). Individual loudness functions.Journal of the Acoustical Society of America,36, 210–213.
Stevens, J. C., &Mack, J. D. (1959). Scales of apparent force.Journal of Experimental Psychology,58, 405–413.
Stevens, J. C., &Tulving, E. (1957). Estimation of loudness by a group of untrained observers.American Journal of Psychology,70, 600–605.
Stevens, S. S. (1956). The direct estimation of sensory magnitudes— loudness.American Journal of Psychology,69, 1–25.
Stevens, S. S. (1957). On the psychophysical law.Psychological Review,64, 153–181.
Stevens, S. S. (1975).Psychophysics. Introduction to its perceptual, neural, and social prospects. New York: Wiley
Susskind, E. C., &Howland, E. W. (1980). Measuring effect magnitude in repeated measures ANOVA designs: Implications for gerontological research.Journal of Gerontology,35, 867–876.
Teghtsoonian, M., &Teghtsoonian, R. (1983). Consistency of individual exponents in cross-modal matching.Perception & Psychophysics,33, 203–214.
Teghtsoonian, R. (1973). Range effects in psychophysical scaling and a revision of Stevens’ law.American Journal of Psychology,86, 3–27.
Teghtsoonian, R., &Teghtssonian, M.(1978). Range and regression effects in magnitude scaling.Perception & Psychophysics,24, 305–314.
Ward, L. M. (1986) Mixed-modality psychophysical scaling: Double cross-modality matching for “difficult” continua.Perception & Psychophysics,39, 407–417
Zegers, F. E. (1986). A family of chance-corrected association coefficients for metric scales.Psychometrika,51, 559–562.
Zegers, F. E., Atenberge, J. M. F. (1985) A family of association coefficients for metric scales.Psychometrika,50, 17–24.
Author information
Authors and Affiliations
Additional information
This research was supported in part by Public Health Service Grant 5R01 MH 20449-06. This paper has benefited considerably from critical suggestions by M. Teghtsoonian, as Action Editor, and two anonymous reviewers
Rights and permissions
About this article
Cite this article
Fagot, R.F., Pokorny, R. Bias effects on magnitude and ratio estimation power function exponents. Perception & Psychophysics 45, 221–230 (1989). https://doi.org/10.3758/BF03210701
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03210701