Judgment of Stimulus Intensity
Weber-Fechner Principle—Detection of “Ratio” of Stimulus Strength. In the mid-1800s,Weber first and Fechner laterproposed the principle that gradations of stimulusstrength are discriminated approximately in proportion to the logarithm of stimulus strength. That is, a personalready holding 30 grams weight in his or her hand can barely detect an additional 1-gram increase in weight. And, when already holding 300 grams, he or she can barely detect a 10-gram increase in weight. Thus, in this instance, the ratio of the change in stimulus strength required for detection remains essentially constant, about 1 to 30, which is what the logarithmic principle means. To express this mathematically.
Interpreted signal strength = Log (Stimulus) + Constant
More recently, it has become evident that the Weber-Fechner principle is quantitatively accurate only for higher intensities of visual, auditory, and cutaneous sensory experience and applies only poorly to most other types of sensory experience. Yet the Weber- Fechner principle is still a good one to remember, because it emphasizes that the greater the background sensory intensity, the greater an additional change must be for the psyche to detect the change.
Power Law. Another attempt by physiopsychologists tofind a good mathematical relation is the following formula, known as the power law.
Interpreted signal strength = K • (Stimulus - k)y
In this formula, the exponent y and the constants K and k are different for each type of sensation.
When this power law relation is plotted on a graph using double logarithmic coordinates, as shown in Figure 47–11, and when appropriate quantitative values for the constants y, K, and k are found, a linear relation can be attained between interpreted stimulus strength and actual stimulus strength over a large range for almost any type of sensory perception.