Stevens' power law

Continuum  Exponent ()  Stimulus conditionLoudness  0.67  Sound pressure of 3000 Hz toneVibration  0.95  Amplitude of 60 Hz on fingerVibration  0.6  Amplitude of 250 Hz on fingerBrightness  0.33  5° target in darkBrightness  0.5  Point sourceBrightness  0.5  Brief flashBrightness  1  Point source briefly flashedLightness  1.2  Reflectance of gray papersVisual length  1  Projected lineVisual area  0.7  Projected squareRedness (saturation)  1.7  Red-gray mixtureTaste  1.3  SucroseTaste  1.4  SaltTaste  0.8  SaccharineSmell  0.6  HeptaneCold  1  Metal contact on armWarmth  1.6  Metal contact on armWarmth  1.3  Irradiation of skin, small areaWarmth  0.7  Irradiation of skin, large areaDiscomfort, cold  1.7  Whole body irradiationDiscomfort, warm  0.7  Whole body irradiationThermal pain  1  Radiant heat on skinTactual roughness  1.5  Rubbing emery clothsTactual hardness  0.8  Squeezing rubberFinger span  1.3  Thickness of blocksPressure on palm  1.1  Static force on skinMuscle force  1.7  Static contractionsHeaviness  1.45  Lifted weightsViscosity  0.42  Stirring silicone fluidsElectric shock  3.5  Current through fingersVocal effort  1.1  Vocal sound pressureAngular acceleration  1.4  5 s rotationDuration  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

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.

Category:Psychology