Stevens's power law

Stevens's power law is an empirical relationship in which perceived stimulus magnitude varies as a power of physical intensity. Its exponent depends on the sensory modality and the stimulus being measured.

Psychophysical scaling: Psychophysical scaling assigns numerical values to sensory experiences and relates them to physical stimulus properties. Stevens's law is a power-function model for scaling perceived magnitude.
Psychophysics: Psychophysics studies quantitative relationships between physical stimuli and sensory or perceptual experience. Stevens's law is a quantitative model within this broader study.
Loudness: Loudness is the perceived strength of an auditory sound. Stevens's law models how sound intensity maps onto judgments of loudness.
Weber–Fechner law: The Weber–Fechner law links perceived change to the relative change in stimulus intensity and predicts logarithmic scaling. Its logarithmic prediction differs from Stevens's modality-dependent power functions.
Magnitude estimation: Magnitude estimation is a method in which people assign numbers proportional to perceived stimulus strength. Stevens developed his law from numerical judgments of sensory magnitude.
Sensation: Sensation is the detection and encoding of physical stimulation by sensory systems. The law concerns the reported magnitude of sensations caused by stimuli.
Brightness: Brightness is the perceived intensity of light emitted or reflected by a surface. Brightness judgments can be related to physical light intensity with a power function.
Signal detection theory: Signal detection theory separates sensitivity to a signal from decision criteria under uncertainty. It addresses detection and discrimination rather than assigning magnitude to sensations.
Psychophysical power law: A psychophysical power law models a sensory judgment as a constant times physical stimulus intensity raised to an exponent. This is the mathematical form used to express Stevens's relationship.
Stimulus intensity: Stimulus intensity is the measurable strength of a physical signal delivered to a sensory system. It supplies the physical quantity whose changes the law relates to perceived magnitude.

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