Stevens' “magnitude estimation” is the most widespread technique for suprathreshold measurement of psychological attributes. Its assumptions, e.g. that subjects are capable of consistently reporting ratios or fractions of sensations, have largely remained untested, though. Recently, Narens (1996) and Luce (2002) developed axiomatic theories of magnitude estimation that provide a theoretical basis for such tests. We evaluated the axioms proposed by Narens in loudness ratio production (and fractionation) tasks. The results indicate that while in principle a ratio scale of loudness exists, the numbers used by subjects in order to describe sensation ratios may not be taken at face value. Recently we have extended this work to the magnitude production of pitch and duration as well as to cross-modality matching.
Other psychophysical/methodological studies in our laboratory investigated how to identify the perceptual attributes that a listener might perceive in a given set of sounds (Wickelmaier & Ellermeier, 2007) and how the auditory system integrates loudness over time (Pedersen & Ellermeier, 2008).
- Ellermeier, W., Kattner, F., & Raum, A. (in press). Cross-modal commutativity of magnitude productions of loudness and brightness. Attention, Perception, & Psychophysics.
- Schlittenlacher, J. & Ellermeier, W. (2021). Continuous magnitude production of loudness. Frontiers in Psychology, 12, 635557. https://doi.org/10.3389/fpsyg.2021.635557
- Birkenbusch, J. & Ellermeier, W. (2016). Axiomatic evaluation of k-multiplicativity in ratio scaling: Investigating numerical distortion. Journal of Mathematical Psychology, 75, 26-33. doi: 10.1016/j.jmp.2015.12.004
- Birkenbusch, J., Ellermeier, W., & Kattner, F. (2015). Octuplicate this interval! Axiomatic examination of the ratio properties of duration perception. Attention, Perception, & Psychophysics, 77, 1767-1780. doi: 10.3758/s13414-015-0846-0
- Kattner, F. & Ellermeier, W. (2014). Fractionation of pitch intervals: An axiomatic study testing monotonicity, commutativity, and multiplicativity in musicians and non-musicians. Attention, Perception, and Psychophysics.76(8), 2508-2521. doi: 10.3758/s13414-014-0674-7
- Pedersen, B. & Ellermeier, W. (2008). Temporal weights in the level discrimination of time-varying sounds. Journal of the Acoustical Society of America 123(2), 963-972. (opens in new tab)
- Wickelmaier, F. & Ellermeier, W. (2007). Deriving auditory features from triadic comparisons. Perception & Psychophysics, 69(2), 287-297. (opens in new tab)
- Zimmer, K. (2005). Examining the validity of numerical ratios in loudness fractionation. Perception & Psychophysics, 67(4), 569-579. (opens in new tab)
- Ellermeier, W. & Faulhammer, G. (2000). Empirical evaluation of axioms fundamental to Stevens' ratio-scaling approach: I. Loudness production. Perception & Psychophysics, 62(8), 1505-1511. https://doi.org/10.3758/BF03212151