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:
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P = perceived intensity of the stimulus
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S = physical magnitude of the stimulus
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k = a scaling constant (depends on units and modality)
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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.
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If n> 1 : Perception increases faster than stimulus (e.g., electric shock)
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If n<1 : Perception increases slower than stimulus (e.g., brightness, loudness)
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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
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Proposed by S. S. Stevens in 1957
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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
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Perceptual scaling in vision, audition, and pain research
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User experience design (e.g., sound volume, brightness controls)
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Marketing psychology (e.g., perceived value or impact)
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Ergonomics and product design
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