Abstract
Five subjects were required in each trial to compare directly two sounds and to indicate which sound was louder. Each of the 64 sounds employed consisted of a combination of one of eight intensity levels of a 2-kHz tone and one of eight intensities of a 5-kHz tone. If, as Fletcher and Munson (1933) argued, loudness is additive for tone combinations in which the frequencies are widely separated, then subjects’ judgments should reflect the summed loudnesses of the 2- and 5-kHz tones in a two-tone combination. Judgments of individual subjects were shown to satisfy the conditions for an additive structure, and individual loudness scales were constructed. These loudness scales varied from subject to subject. Since this paired comparison procedure minimized response biases, the results suggest substantial individual differences in the sensory representation of sound intensity. The relations among sensory scales derived from other structured sensory judgments, such as binaural loudness, are discussed.
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Algom, D., &Marks, L. E. (1984). Individual differences in loudness processing and loudness scales.Journal of Experimental Psychology: General,113, 571–593.
Anderson, N. H. (1970). Functional measurement and psychophysical judgment.Psychological Review,77, 153–170.
Anderson, N. H. (1974). Algebraic models in perception. In E. C. Carterette & M. P. Friedman (Eds.),Handbook of perception: Vol. II. Psychophysical judgment and measurement (pp. 215–298). New York: Academic Press.
Carterette, E. C., &Anderson, N. H. (1979). Bisection of loudness.Perception & Psychophysics,26, 265–280.
Curtis, D. W., Attneave, F., &Harrington, T. L. (1968). A test of a two-stage model of magnitude judgment.Perception & Psychophysics,3, 25–31.
Curtis, D. W., &Rule, S. J. (1972). Magnitude judgments of brightness and brightness difference as a function of background reflectance.Journal of Experimental Psychology,95, 215–222.
Fagot, R. F., Stewart, M. R., &Kleinknecht, R. E. (1975). Representations for biased numerical judgments.Perception & Psychophysics,17, 309–319.
Falmagne, J.-C. (1976). Random conjoint measurement and loudness summation.Psychological Review,83, 65–79.
Fletcher, H., &Munson, W. A. (1933). Loudness, its definition, measurement and calculation.Journal of the Acoustical Society of America,5, 82–108.
Gigerenzer, G., &Strube, G. (1983). Are there limits to binaural additivity of loudness?Journal of Experimental Psychology: Human Perception & Performance,9, 126–136.
Green, D. M., &Luce, R. D. (1974). Variability of magnitude estimates: A timing theory analysis.Perception & Psychophysics,15, 291–300.
Hays, W. L. (1973).Statistics for the social sciences. New York: Holt, Rinehart & Winston.
Hubert, L. (1976). Seriation using asymmetric proximity measures.British Journal of Mathematical & Statistical Psychology,29, 32–52.
Kendall, M. G., &Babington-Smith, B. (1939). On the method of paired comparisons.Biometrika,31, 324–345.
Krantz, D. H. (1972). A theory of magnitude estimation and crossmodality matching.Journal of Mathematical Psychology,9, 168–199.
Krantz, D. H., Luce, R. D., Suppes, P., &Tversky, A. (1971).Foundations of measurement: Vol. 1. Additive and polynomial representations. New York: Academic Press.
Levelt, W. J. M., Riemersma, J. B., &Bunt, A. A. (1972). Binaural additivity of loudness.British Journal of Mathematical & Statistical Psychology,25, 51–68.
Luce, R. D., &Green, D. M. (1978). Two tests of a neural attention hypothesis for auditory psychophysics.Perception & Psychophysics,23, 363–371.
Luce, R. D., &Tukey, J. W. (1964). Simultaneous conjoint measurement: A new type of fundamental measurement.Journal of Mathematical Psychology,1, 1–27.
Marks, L. E. (1974).Sensory processes: The new psychophysics. New York: Academic Press.
Marks, L. E. (1978a). Binaural summation of the loudness of pure tones.Journal of the Acoustical Society of America,64, 107–113.
Marks, L. E. (1978b). PHONION: Translation and annotations concerning loudness scales and the processing of auditory intensity. In J. J. Castellan & F. Restle (Eds.),Cognitive theory (Vol. 3, pp. 7–31). Hillsdale, NJ: Erlbaum.
Marks, L. E. (1979a). Sensory and cognitive factors in judgments of loudness.Journal of Experimental Psychology: Human Perception & Performance,5, 426–443.
Marks, L. E. (1979b). A theory of loudness and loudness judgments.Psychological Review,86, 256–285.
Marks, L. E. (1980). Binaural summation of loudness: Noise and twotone complexes.Perception & Psychophysics,27, 489–498.
Popper, R., Parker, S., &Galanter, E. (1986). Dual loudness scales in individual subjects.Journal of Experimental Psychology: Human Perception & Performance,12,61–69.
Ross, S. (1967). Matching functions and equal-sensation contours for loudness.Journal of the Acoustical Society of America,42, 778–793.
Rule, S. J., &Curtis, D. W. (1982). Levels of sensory and judgmental processing: Strategies for evaluation of a model. In B. Wegener (Ed.),Social attitudes and psychophysical measurement (pp. 107–122). Hillsdale, NJ: Erlbaum.
Rule, S. J., Curtis, D. W., &Markley, R. P. (1970). Input and output transformations from magnitude estimation.Journal of Experimental Psychology,86, 343–349.
Rule, S. J., Laye, R. C., Curtis, D. W. (1974). Magnitude judgments and difference judgments of lightness and darkness: A twostage analysis.Journal of Experimental Psychology,103, 1108–1114.
Scharf, B. (1970). Critical bands. In J. V. Tobias (Ed.),Foundations of modern auditory theory (Vol. 1, pp. 157–202). New York: Academic Press.
Schneider, B. (1980a). Individual loudness functions determined from direct comparisons of loudness intervals.Perception & Psychophysics,27, 493–503.
Schneider, B. (1980b). A technique for the nonmetric analysis of paired comparisons of psychological intervals.Psychometrika,45,357–372.
Schneider, B., &Lane, H. (1963). Ratio scales, category scales, and variability in the production of loudness and softness.Journal of the Acoustical Society of America,35, 1953–1961.
Schneider, B., Parker, S., &Stein, D. (1974). The measurement of loudness using direct comparisons of sensory intervals.Journal of Mathematical Psychology,11, 259–273.
Schneider, B., Parker, S., Valenti, M., Farrell, G., &Kanow, G. (1978). Response bias in category and magnitude estimation of difference and similarity for loudness and pitch.Journal of Experimental Psychology: Human Perception & Performance,4, 483–496.
Schneider, B., Wright, A. A., Edelheit, W., Hock, P., &Humphrey, C. (1972). Equal loudness contours derived from sensory magnitude judgments.Journal of the Acoustical Society of America,51, 1951–1959.
Slater, P. (1961). Inconsistencies in a schedule of paired comparisons.Biometrika,48, 303–312.
Stevens, J. C., &Guirao, M. (1964). Individual loudness functions.Journal of the Acoustical Society of America,36, 2210–2213.
Teghtsoonian, R. (1973). Range effects in psychophysical scaling and a revision of Stevens’ law.American Journal of Psychology,86, 3–27.
Wanschura, R., &Dawson, W. (1974). Regression effect and individual power functions over sessions.Journal of Experimental Psychology,102, 806–812.
Young, F. W. (1970). Nonmetric multidimensional scaling: Recovery of metric information.Psychometrika,35, 455–473.
Zwicker, E., Flottorp, G., &Stevens, S. S. (1957). Critical bandwidth in loudness summation.Journal of the Acoustical Society of America,29, 548–557.
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Preparation of this article was supported in part by the Natural Sciences and Engineering Research Council of Canada.
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Schneider, B. The additivity of loudness across critical bands: A conjoint measurement approach. Perception & Psychophysics 43, 211–222 (1988). https://doi.org/10.3758/BF03214203
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DOI: https://doi.org/10.3758/BF03214203