Stevens's 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 | Saccharin |
| 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 an empirical relationship in psychophysics between an increased intensity or strength in a physical stimulus and the perceived magnitude increase in the sensation created by the stimulus. It is often considered to supersede the Weber–Fechner law, which is based on a logarithmic relationship between stimulus and sensation, because the power law describes a wider range of sensory comparisons, down to zero intensity.
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 I is the intensity or strength of the stimulus in physical units (energy, weight, pressure, mixture proportions, etc.), ψ(I) is the magnitude of the sensation evoked by the stimulus, a is an exponent that depends on the type of stimulation or sensory modality, and k is a proportionality constant that depends on the units used.
A distinction has been made between local psychophysics, where stimuli can only be discriminated with a probability around 50%, and global psychophysics, where the stimuli can 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 adjacent table lists the exponents reported by Stevens.