Stevens’ Power Law

Stevens’ Power Law is a fundamental principle in psychophysics that describes the relationship between the magnitude of a physical stimulus and the perceived intensity of that stimulus.


 Definition

Stevens’ Power Law states that:

P=k⋅Sn 

Where:

  • P = perceived intensity of the stimulus

  • S = physical magnitude of the stimulus

  • k = a scaling constant (depends on units and modality)

  • n = exponent that varies by type of stimulus


 What It Means

Unlike Fechner’s Law (which assumes a logarithmic relationship), Stevens’ Power Law suggests that perceived intensity grows as a power function of the actual stimulus.

  • If n> 1 : Perception increases faster than stimulus (e.g., electric shock)

  • If n<1 : Perception increases slower than stimulus (e.g., brightness, loudness)

  • If n=1: Perception grows linearly with stimulus (e.g., length)


 Examples of Exponents n

Sensory Modality Approx. nn Value Interpretation
Electric shock ~3.5 Perceived intensity rises very rapidly
Brightness ~0.33 Brightness perception increases slowly
Loudness ~0.6 Loudness perception increases moderately
Weight (heaviness) ~1.45 Heaviness perception increases more steeply
Line length ~1.0 Perceived length matches physical length

 Origin

  • Proposed by S. S. Stevens in 1957

  • Based on magnitude estimation experiments, where subjects rated stimulus intensity on a numerical scale


 Comparison: Fechner vs. Stevens

Feature Fechner’s Law Stevens’ Power Law
Function Type Logarithmic Power
Based On Just-noticeable differences (JNDs) Magnitude estimation
Flexibility Limited (same form for all senses) More flexible (exponent varies)
Empirical Accuracy Less accurate for extreme ranges More accurate across wider stimulus ranges

 Applications

  • Perceptual scaling in vision, audition, and pain research

  • User experience design (e.g., sound volume, brightness controls)

  • Marketing psychology (e.g., perceived value or impact)

  • Ergonomics and product design

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