Stevens' Power Law

In 1957, after dozens of experiments on direct scaling, such as magnitude estimation, appeared in the literature, S. S. Stevens proposed a new law to relate sensation magnitude to stimulus intensity:

So when plotted on log-log axes, the power law plots as a straight line with a slope of the exponent.

The exponent can be greater than one representing a positively accelerated or expansive function or it can be less than one representing a negatively accelerated or compressive function. We can compare this to Fechner's law which is compressive. There are functions, such as the perception of line length that have exponents equal to 1 showing a linear relationship between stimulus physical magnitude and perceptual magnitude.

Is Stevens' law a replacement of Fechner's Law? The answer to this question must involve questions about the assumptions underlying Fechner's Law (all jnd's are alike) and the interpretation and application of these laws.

Here are a couple of graphs showing power functions:

For fun, here is a table of exponents collected by Stevens.

Continuum
Measured 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 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 Sacchrine
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 irradiaton
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 Lifed 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-sec rotation
Duration 1.1 White noise stimuli

 Continue on to Chapter 7