Psychophysical Ratio Scaling
Measurement of physical properties on ratio scales has always been a highly desirable achievement, since these scales can contain the characteristics of order, distance, and origin while retaining maximal correspondence with the number system. Methods for constructing ratio scales of sensation have been used extensively in the past 35 years. However, as far back as 1888, Merkel was interested in finding the stimulus that doubled sensation. Merkel had observers adjust a variable stimulus so that its sensation was twice as great as the sensation produced by a fixed stimulus. A similar procedure used by Fullerton and Cattell ( 1892) required observers to adjust a stimulus to produce a sensation that was some fraction or multiple of the sensation produced by a standard stimulus. These procedures result in ratio scales of sensation when the ratio of one sensation magnitude to another can be specified. It was not until the 1930s, when acoustical engineers became concerned with the problem of numerically specifying psychological loudness, that psychologists became interested in ratio measurements of sensation.
The practical problem of measuring loudness arose out of an obvious failure of Fechner's law. Acoustical engineers had assumed the validity of Fechner's law and adopted the decibel scale, which is a logarithmic scale of sound energy. It was hoped that, with this new scale, sounds could be specified in numbers reflecting the magnitude of the sensations they produced. It soon became apparent, however, that a sound of 60 dB was much more than twice as loud as a sound of 30 dB. It was through the development of special techniques for measuring loudness that psychophysics was supplied with the several ratio scaling methods sub