First ISCA ITRW on Auditory Quality of Systems

April 23-25, 2003
Akademie Mont-Cenis, Germany

Direct Scaling of Sensations: Are Subjects Able to Produce Consistent, and Meaningful, Numerical Ratios?

Karin Zimmer, Oliver Baumann

Sound Quality Research Unit, Dept. of Acoustics, Aalborg University, Denmark

In psychophysical scaling, direct estimation procedures like e.g. magnitude estimation, magnitude production, or fractionation, play a dominant role. S.S. Stevens [1, 2] introduced the idea that subjects are able to directly report a numerical value which represents the sensation magnitude experienced. Following his approach, the numerals assigned can be taken at face value, i.e. they possess all the mathematical properties of the numbers they signify. Only recently, theories analyzing the foundation of Stevens’ approach [3, 4] have detailed which basic empirical conditions have to be fulfilled in order to meet this far-reaching assumption, and to relate numerals and numbers in a meaningful way. In the present investigation, these fundamental conditions were evaluated using loudness fractionations of 1 kHz-tones. The subjects’ task was to adaptively adjust the loudness of a tone so that it reached a certain pre-specified fraction of the loudness of a reference tone. Results of the first experiment suggest, that listeners are able to make such adjustments on a ratio-scale level. It was not possible, however, to interpret the nominal fractions used in the task as ’true,’ scientific numbers. Thus, Stevens’ fundamental assumption that a subject can directly assess the sensation magnitude a stimulus elicits did not hold. The second experiment investigated the possibility of establishing a well-defined transformation function proposed by [4] that relates the overt numerals to the latent mathematical numbers. First results suggest that this is not possible for all of the subjects.


  1. Stevens, S.S., "The direct estimation of sensory magnitudes - loudness", American Journal of Psychology, 69:1-25, 1956.
  2. Stevens, S.S., Psychophysics: Introduction to ist perceptual, neural, and social prospects, Wiley, New York, 1975.
  3. Narens, L., "A theory of ratio magnitude estimation", Journal of Mathematical Psychology, 40:109:129, 1996.
  4. Luce, R.D., "A psychophysical theory of intensity proportions, joint presentations, and matches", Psychological Review, 109(3):520-532, 2002.

Full Paper

Bibliographic reference.  Zimmer, Karin / Baumann, Oliver (2003): "Direct scaling of sensations: Are subjects able to produce consistent, and meaningful, numerical ratios?", In AQS-2003, 85-90.