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Psychophysical Functions

Early psychophysicists found that the larger the magnitude of the stimulus (for example, the brighter the light), the larger was the just-noticeable difference (JND). For example, if you compare a 25-watt bulb with a 50-watt light bulb, they look very different. But if you compare a 175-watt bulb to a 200-watt bulb, they look almost the same. In general, we are less sensitive to differences in signal strength as the intensity of a stimulus increases. This relationship was first summarized by Ernst Weber (VAY-ber) in 1834. His equation was called Weber's Law.

What was the general idea behind Weber's Law?

Gustav Fechner

Weber's Law states that the JND increases in direct proportion to the intensity of a stimulus. But often this is not true when stimuli approach extreme values. In 1860 Gustav Fechner proposed a new law to account for such curves. Fechner's Law specified that psychophysical functions relating perceived magnitude of a stimulus to physical intensity would follow a logarithmic relationship. A logarithmic relationship produces a curve that drops as the magnitude of a stimulus approaches extreme values. (The curve in the following figure labeled "brightness" shows such a relationship.)

What problem in Weber's Law did Fechner's Law address?

Fechner's Law provides a better fit than Weber's Law for many types of stimuli. Fechner won respect in the scientific world, as the result of his careful research. Some historians of science say that Fechner, rather than Wundt, launched experimental psychology with the publication of a book about 10 years before Wundt started his laboratory.

Psychophysical curves produced by different types of stimuli

While many sensory stimuli fit Fechner's law, some do not. Electric shock produces a curve that goes the wrong direction. The line labeled "electric shock" on the graph shows this. People become more sensitive to electricity as the magnitude of a shock goes up. The same is true of judgments of heaviness.

What was the general idea of Stevens' Law?

The American psychologist S. S. Stevens proposed a formula that accounted for all these curves, even the curve for electric shock. He suggested that the strength of a sensation was related to the intensity of a physical stimulus raised to some power. In other words, he proposed an exponential function. If the exponent were greater than one, the line would curve up, as with the lines labeled "electric shock" and "heaviness." If the exponent was one, the result was a straight line as described by Weber's Law. If the exponent was less than one, the result was a downward sloping curves like those predicted by Fechner.

Stevens's work was done in the 1960s. It represented an elegant solution to the problem of defining psychophysical relationships. However, by the time Stevens's Power Law replaced Fechner's Law, the whole field of psychophysics was undergoing a dramatic change because of a new approach called the Theory of Signal Detection.

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