Stevens' Power Law

Stevens' power law is a proposed relationship between the magnitude of a physical stimulus and its perceived intensity or strength. It is often considered to supersede the Weber–Fechner law on the basis that it describes a wider range of sensations, although critics argue that the validity of the law is contingent on the virtue of approaches to the measurement of perceived intensity that are employed in relevant experiments. In addition, a distinction has been made between (i) local psychophysics, where stimuli are discriminated only with a certain probability, and (ii) global psychophysics, where the stimuli would be discriminated correctly with near certainty (Luce & Krumhansl, 1988). The Weber–Fechner law and methods described by L.L. Thurstone are generally applied in local psychophysics, whereas Stevens' methods are usually applied in global psychophysics.

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 1957.

The general form of the law is

where is the magnitude of the physical stimulus, ψ(I) is the psychophysical function relating to the subjective magnitude of the sensation evoked by the stimulus, a is an exponent that depends on the type of stimulation and k 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.