Stevens' Power Law

Background

S.S. Stevens (1957) proposed that the relationship between physical stimulus intensity and perceived magnitude follows a power law:

ψ = k · Iⁿ

where ψ is perceived magnitude, I is physical intensity, k is a constant, and n is the power law exponent. The exponent varies by sensory dimension:

Line length: n ≈ 1.0 (perception matches reality)
Area: n ≈ 0.7 (we underestimate area)
Brightness: n ≈ 0.33 (compressive)
Electric shock: n ≈ 3.5 (expansive — ouch!)

Magnitude Estimation

The method of magnitude estimation asks participants to assign numbers proportional to perceived intensity. A standard stimulus is given a fixed value (the modulus), and participants rate test stimuli relative to it.

References

Stevens, S.S. (1957). On the psychophysical law. Psychological Review, 64, 153–181.
Stevens, S.S. (1961). To honor Fechner and repeal his law. Science, 133, 80–86.
Gescheider, G.A. (1997). Psychophysics: The Fundamentals (3rd ed.). Lawrence Erlbaum.

You'll see horizontal lines of varying length. A standard line is assigned the value 10.

For each test line, type a number that represents its perceived length relative to the standard.

If the test line looks twice as long as the standard, type 20. If it looks half as long, type 5. Use any positive number.

The standard will always be visible for reference. There are 30 trials (10 lengths × 3 repetitions).

Stevens' Power Law

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