power law

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Any law expressed by a mathematical power function, especially the psychophysical law that was advocated from 1953 onwards by the US psychologist S(tanley) S(mith) Stevens (1906–73) and discussed by him in an influential article in the journal Psychological Review in 1957, a century after it was first proposed by the Belgian physicist Joseph Antoine Ferdinand Plateau (1801–83), and that largely replaced Fechner's law. According to the power law, the magnitude of a sensation is a power function of the intensity of the stimulus causing it, so that equal proportional increases in sensation correspond to equal proportional increases in stimulus intensity, the two proportions not necessarily being the same. It is usually expressed by the equation ψ = n, where ψ is the magnitude of the sensation, φ is the physical intensity of the stimulus, k is a constant scaling factor that depends on the units of measurement, and n is an exponent or power that is constant for a given type of sensory experience but that varies from one type of sensation to the next, with n = 0.33 for visual brightness perception, n = 0.67 for loudness perception, n = 1.45 for heaviness perception of lifted weights, n = 1.00 for visual length perception, of which people have much experience, and so on. Also called Stevens's law or Stevens's power law. See also prospect theory, psychophysical function. [So called because φ is raised to the power of n]

Subjects: Psychology.

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