Stevens' Power Law

Stevens's power law is a mathematical description of the relationship between the physical intensity of a stimulus and the intensity of the sensation a person perceives from it, expressed as psi equals k times I raised to the power a, meaning perceived sensation grows as a power function of the actual physical stimulus intensity rather than in a strictly logarithmic pattern. The psychophysicist Stanley Smith Stevens revived and formalized the power-law relationship, publishing supporting empirical evidence in 1957, building on a possibility that had already been suggested by researchers in the nineteenth century. Stevens's law is presented as superseding the earlier Weber-Fechner law of psychophysics because it remains accurate down to very low stimulus intensities near zero and applies consistently across a wide range of different sensory modalities, from the perceived loudness of sound and brightness of light to taste, touch and thermal sensation. The specific exponent in the power-law relationship differs by sensory modality, for instance a reported exponent of about 0.67 for loudness compared with about 3.5 for the sensation of electric shock, reflecting the fact that perceived intensity grows at very different rates in different sensory channels; researchers establish these values by having human subjects directly estimate the perceived magnitude of stimuli relative to one another.