Stevens' power law
| Continuum | Exponent ([math]\displaystyle{ a }[/math]) | Stimulus condition |
|---|---|---|
| Loudness | 0.67 | Sound pressure of 3000 Hz tone |
| Vibration | 0.95 | Amplitude of 60 Hz on finger |
| Vibration | 0.6 | Amplitude of 250 Hz on finger |
| Brightness | 0.33 | 5° target in dark |
| Brightness | 0.5 | Point source |
| Brightness | 0.5 | Brief flash |
| Brightness | 1 | Point source briefly flashed |
| Lightness | 1.2 | Reflectance of gray papers |
| Visual length | 1 | Projected line |
| Visual area | 0.7 | Projected square |
| Redness (saturation) | 1.7 | Red-gray mixture |
| Taste | 1.3 | Sucrose |
| Taste | 1.4 | Salt |
| Taste | 0.8 | Saccharine |
| Smell | 0.6 | Heptane |
| Cold | 1 | Metal contact on arm |
| Warmth | 1.6 | Metal contact on arm |
| Warmth | 1.3 | Irradiation of skin, small area |
| Warmth | 0.7 | Irradiation of skin, large area |
| Discomfort, cold | 1.7 | Whole body irradiation |
| Discomfort, warm | 0.7 | Whole body irradiation |
| Thermal pain | 1 | Radiant heat on skin |
| Tactual roughness | 1.5 | Rubbing emery cloths |
| Tactual hardness | 0.8 | Squeezing rubber |
| Finger span | 1.3 | Thickness of blocks |
| Pressure on palm | 1.1 | Static force on skin |
| Muscle force | 1.7 | Static contractions |
| Heaviness | 1.45 | Lifted weights |
| Viscosity | 0.42 | Stirring silicone fluids |
| Electric shock | 3.5 | Current through fingers |
| Vocal effort | 1.1 | Vocal sound pressure |
| Angular acceleration | 1.4 | 5 s rotation |
| Duration | 1.1 | White noise stimuli |
Stevens' power law is a proposed relationship between the magnitude of a physical stimulus and the intensity or strength that people feel.
Most people think that it describes a wider range of sensations than Weber-Fechner law. But critics argue that the validity of the law is not sure.
The theory is named after psychophysicist Stanley Smith Stevens (1906–1973). Although the idea of a power law had been suggested by 19th century researchers, Stevens is credited with reviving the law and publishing a body of psychophysical data to support it in 1956.
The general form of the law is
- [math]\displaystyle{ \psi(I) = k I ^a , \,\! }[/math]
where [math]\displaystyle{ I }[/math] is the magnitude of the physical stimulus, [math]\displaystyle{ \psi }[/math] is the psychophysical function capturing sensation (the subjective size of the stimulus), [math]\displaystyle{ a }[/math] is an exponent that depends on the type of stimulation and [math]\displaystyle{ k }[/math] is a proportionality constant that depends on the type of stimulation and the units used.
The table to the right lists the exponents reported by Stevens.
References
- Ellermeier, W., Faulhammer, G. (2000). Empirical evaluation of axioms fundamental to Stevens's ratio-scaling approach: I. Loudness production. Perception & Psychophysics, 62, 1505–1511.
- Green, D. M., & Luce, R. D. (1974). Variability of magnitude estimates: a timing theory analysis. Perception & Psychophysics, 15, 291–300.
- Luce, R. D. (2002). A psychophysical theory of intensity proportions, joint presentations, and matches. Psychological Review, 109, 520–532.
- Narens, L. (1996). A theory of ratio magnitude estimation. Journal of Mathematical Psychology, 40, 109–129.
- Smelser, N. J., & Baltes, P. B. (2001). International encyclopedia of the social & behavioral sciences. pp. 15105–15106. Amsterdam; New York: Elsevier. ISBN 0-08-043076-7.
- Steingrimsson, R., & Luce, R. D. (2006). Empirical evaluation of a model of global psychophysical judgments: III. A form for the psychophysical function and intensity filtering. Journal of Mathematical Psychology, 50, 15–29.
- Stevens, S. S. (1957). On the psychophysical law. Psychological Review 64(3):153–181. PMID 13441853.
- Zimmer, K. (2005). Examining the validity of numerical ratios in loudness fractionation. Perception & Psychophysics, 67, 569–579.