Abstract
To take account of the observed lack of fit of the power law near thresh-old intensities, two different modifications of the power law have been proposed by various investigators. In this paper, both of these two laws are derived as a special case of a generalized power function for ratio scaling. A method is presented for discriminating between the special laws which provides (i) a prescription for the manipulation of independent variables, and (ii) specification of theoretical curves to which empirical curves are to be compared. Maximum-likelihood estimators are derived for the exponents of the special laws under the assumption that the observed subjective ratios are log normal.
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This research was supported in part by National Science Foundation Grant G19210 and in part by a Public Health Service Special Fellowship (No. MSP-15800), from the National Institutes of Health, Public Health Service. During the tenure of this fellowship, facilities of the Institute for Human Learning, University of California, Berkeley, were made available to me. The computing was carried out at the University of California Computer Center and the University of Oregon Statistical Laboratory and Computing Center. I have benefited appreciably from numerous discussions of this research with Manard Stewart.
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Fagot, R.F. Alternative power laws for ratio scaling. Psychometrika 31, 201–214 (1966). https://doi.org/10.1007/BF02289507
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DOI: https://doi.org/10.1007/BF02289507