Abstract
Suppose magnitude estimates on successive trials preserve the ratio of random internal representations of the corresponding signals. Then the mean response generally exhibits drift over trials; sequential dependencies usually exist in which case the mean response ratio is not a function of intensity ratio; however, a modified function is if the mean representation is a power function of intensity. Relevant loudness data are cited. The special timing representation is wrong if the sample size is just a function of the signal, but is viable if it is one of two sizes depending on the size of the intensity ratio to the preceding signal. This attention hypothesis is an analogue for intensity of the critical-band notion for frequency.
This work was supported in part by National Science Foundation grants to the University of California, Irvine and San Diego.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Comrey, A. L. A proposed method for absolute ratio scaling. Psychometrika, 1950, 15, 317–325.
Cross, D. V. Sequential dependencies and regression in psychophysical judgments. Perception and Psychophysics, 1973, 14, 547–552.
Garner, W. R. An informational analysis of absolute judgments of loudness. Journal of Experimental Psychology, 1953, 46, 373–380.
Green, D. M., & Luce, R. D. Variability of magnitude estimates: A timing theory analysis. Perception and Psychophysics, 1974, in press.
Holland, M. K., & Lockhead, G. R. Sequential effects in absolute judgments of loudness. Perception and Psychophysics, 1968, 3, 409–414.
Krantz, D. H. A theory of magnitude estimation and cross-modality matching. Journal of Mathematical Psychology, 1972, 9, 168–199.
Luce, R. D., & Green, D. M. A neural timing theory for response times and the psychophysics of intensity. Psychological Review, 1972, 79, 14–57.
Luce, R. D., & Green, D. M. The response ratio hypothesis for magnitude estimation. Journal of Mathematical Psychology, 1974, 11, 1–14.
Luce, R. D., & Mo, S. S. Magnitude estimation of heaviness and loudness by individual subjects: A test of a probabilistic response theory. British Journal of Mathematical and Statistical Psychology, 1965, 18, 159–174.
Marley, A. A. T. Internal state models for magnitude estimation and related experiments. Journal of Mathematical Psychology, 1972, 9, 306–319.
Schneider, B., & Lane, H. Ratio scales, category scales, and variability in the production of loudness and softness. Journal of the Acoustical Society of America, 1963, 35, 1953–1961.
Sjöberg, L. On ratio estimation. Report 191. Psychological Laboratory, University of Stockholm, 1962.
Sjöberg, L. Three models for the analysis of subjective ratios. The Scandinavian Journal of Psychology, 1971, 12, 217–240.
Stevens, S. S. On the psychophysical law. Psychological Review, 1957, 64, 153–181.
Stevens, S. S. On the validity of the loudness scale. Journal of the Acoustical Society of America, 1959, 31, 995–1003.
Stevens, S. S. Toward a resolution of the Fechner-Thurstone legacy. Psychometrika, 1961, 26, 35–47. (a)
Stevens, S. S. To honor Fechner and repeal his law. Science, 1961, 133, 80–86. (b)
Stevens, S. S. Issues in psychophysical measurement. Psychological Review, 1971, 78, 426–450.
Svenson, O., & Åkesson, C. Å. Fractional and multiple estimates in ratio scaling. Report 202. Psychological Laboratory, University of Stockholm, 1966. (a)
Svenson, O., & Åkesson, C. Å. On a relation between fractional and multiple estimates in ratio scaling. Report 220. Psychological Laboratory, University of Stockholm, 1966. (b)
Svenson, O., & Åkesson, C. Å. A further note on fractional and multiple estimates in ratio scaling. Report 224. Psychological Laboratory, University of Stockholm, 1967.
Torgerson, W. S. Theory and methods of scaling. New York: Wiley, 1958.
Ward, L. M. Category judgments of loudness in the absence of an experimental-induced identification function: Sequential effects and power functions fit. Journal of Experimental Psychology, 1972, 94, 179–187.
Ward, L. M. Repeated magnitude estimations with a variable standard: Sequential effects and other properties. Perception and Psychophysics, 1973, 13, 193–200.
Ward, L. M. & Lockhead, G. R. Sequential effects and memory in category judgments. Journal of Experimental Psychology, 1970, 84, 27–34.
Ward, L. M. & Lockhead, G. R. Response system processes in absolute judgment. Perception and Psychophysics, 1971, 9, 73–78.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1974 D. Reidel Publishing Company, Dordrecht-Holland
About this chapter
Cite this chapter
Luce, R.D., Green, D.M. (1974). Ratios of Magnitude Estimates. In: Moskowitz, H.R., Scharf, B., Stevens, J.C. (eds) Sensation and Measurement. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-2245-3_9
Download citation
DOI: https://doi.org/10.1007/978-94-010-2245-3_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-2247-7
Online ISBN: 978-94-010-2245-3
eBook Packages: Springer Book Archive