Extracting magnitude estimations of loudness from pairwise judgments

Four problems limit widespread applications of magnitude estimation scales. There is first a serious question about the meaning of the judgments. Second, the judgments appear to be intrinsically unreliable. Third, amalgamation methods used to strike averages from several observers are poorly understood. Finally, it is difficult to know how to evaluate a single entity as distinct from a stimulus domain by these methods. A new psychophysical method is described and demonstrated that can scale any perceptual or attitudinal continuum. Observers give a numerical estimate of the magnitude of a randomly selected stimulus relative to another such stimulus to which a computer has assigned a random number. The stimulus pairs vary at random from trial to trial. Ratios of these computer-person number pairs estimate the slope of the psychophysical function. The slope lets us normalize the judgments which can then be mapped onto the stimulus domain. Loudness functions for individuals are shown with none of the cusps or singularities of traditional magnitude estimations from individuals. [Work supported in part by NASA.]