Stevens' power law

|Continuum||Exponent ()||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 sensation<nowiki/>s 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
where   is the magnitude of the physical stimulus,  is the psychophysical function capturing sensation (the subjective size of the stimulus),  is an exponent that depends on the type of stimulation and  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. .
- 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.