A test of the generality of Stevens' power function using the method of magnitude production



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A test of the generality of Stevens' power law was undertaken, using the method of magnitude production. Finger span was selected as the continuum for this test because it represented a continuum in which a scale has been constructed by Stevens (Stevens & Stone, 1959) using another method, the method of magnitude estimation. Rather than presenting a series of blocks and having Ss assign numbers to them which represent scale values, as the magnitude estimating method prescribes, a procedure was designed in which estimates made by Ss involved kinesthetic manipulation of a "continuous-stimulus object." For these purposes a 76 cm tapered block was used, gradually increasing in width from 5 mm to 110 mm. This served as the variable stimulus, and a single block, 15.5 mm in width, served as the standard. The standard was assigned the arbitrary scale value 10, and it was the Ss' task to find on the tapered block the corresponding positions of the numbers 20, 30, 45, 60, 75, 90, 105, and 120. A total of 30 Ss participated in the experiment. Each S made four judgements about each of the eight stimuli, making a total of 120 judgements. Comparisons were made of functions obtained by means of Stevens' power function, a logarithmic function, and a derived power function. In addition, questions involving arithmetic versus geometric means, and the role of individual psychophysical functions as power functions were considered. The scale obtained demonstrated that apparent thickness was a positively accelerated function of stimulus magnitude. The derived power equation was found to be by far the best description of the function.



Perception, Psychophysiology