Abstract
This paper is concerned with the scaling method of “ratio estimation.” The simple theory that equates reported ratio judgments to ratios of psychological magnitudes is first considered, then two close relatives of this theory are formulated, each of which places weaker constraints on the structure of the data. Structural conditions are stated that express the relations that must hold among observed ratio judgments for each of the models. The models proposed are “cumulative” in the sense that the second is a weakened version of the first, and the third a weakened version of the second. A special feature of the models is that they may be tested entirely in terms of observables, avoiding the necessity of scale construction prior to testing. Tests were carried out on data from 9 published studies. The strongest model, typically used in scale construction using ratio estimation data, was generally inadequate, showing large systematic errors. However, the weakest version generally passed the tests of internal consistency, and the model equation provided a basis for constructing ratio scales utilizing bias parameters.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Reference Note
Mashhour, M.On the validity of scales derived by ratio and magnitude estimation methods. Report of the Psychology Laboratory, University of Stockholm, 1961, No. 105.
References
Bartko, J. J. On various intraclass correlation reliability coefficients.Psychological Bulletin, 1976,83, 762–765.
Eisler, H. Similarity in the continuum of heaviness with some methodological and theoretical considerations.Scandinavian Journal of Psychology, 1960,1, 69–81.
Eisler, H., &Ekman, G. A mechanism of subjective similarity.Acta Psychologica, 1959,16, 1–10.
Ekmas, G. Two generalized ratio scaling methods.Journal of Psychology, 1958,45, 287–295.
Ekman, G., Goude, G., &Waern, Y. Subjective similarity in two perceptual continua.Journal of Experimental Psychology, 1961,61, 222–227.
Engen.T., &Lindström, C. O. Psychophysical scales of the odor intensity of amyl acetate.Scandinavian Journal of Psychology, 1963,4, 23–28.
Fagot, R. F., &Stewart, M. Tests of product and additive scaling axioms.Perception & Psychophysics, 1969,5, 117–123.
Fagot, R. F., Stewart, M. R., &Kleinknecht, R. E. Representations for biased numerical judgments.Perception & Psychophysics, 1975,17, 309–319.
Goude, G.On fundamental measurement in psychology. Stockholm: Almqvist & Wiksell, 1962.
Krantz, D. H. A theory of magnitude estimation and cross-modality matching.Journal of Mathematical Psychology, 1972,9, 168–199.
Lilienthal, M. G., &Dawson, W. E. Inverse cross-modality matching: A test of ratio judgment consistency for group and individual data.Perception & Psychophysics, 1976,19, 252–260.
Marks, L. E.Sensory processes, the new psychophysics. New York: Academic Press, 1974.
Mashhour, M.Psychophysical relations in the perception of velocity. Stockholm: Almqvist & Wiksell, 1964.
Mulaik, S. A.The foundations of factor analysis. New York: McGraw-Hill, 1972.
Sjöberg, L. Three models for the analysis of subjective ratios.Scandinavian Journal of Psychology, 1971,12, 217–240.
Stevens, S. S. Problems and methods of psychophysics.Psychological Bulletin, 1958,55, 177–196.
Stevens, S. S., &Galanter, E. H. Ratio scales and category scales for a dozen perceptual continua.Journal of Experimental Psychology, 1957,54, 377–411.
Author information
Authors and Affiliations
Additional information
Work on this paper was carried out, in part, during the author’s tenure as a Fellow at the Netherlands Institute for Advanced Study, Wassenaar, Holland.
An erratum to this article is available at http://dx.doi.org/10.3758/BF03206112.
Rights and permissions
About this article
Cite this article
Fagot, R.F. A theory of relative judgment. Perception & Psychophysics 24, 243–252 (1978). https://doi.org/10.3758/BF03206095
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.3758/BF03206095