Subjective Rating and Apparent Magnitude

In category-scaling studies of television impairments, the psychometric functions describing the relationship between subjective rating and stimulus magnitude generally take a simple logistic form. A similar result tends to be approximated in experiments with other kinds of stimuli described by Stevens & Galanter: (1957) as prothetic. It leads to the following simple relationship between category scaling and ratio scaling: t = 1/(1 + N -k ), Here t is subjective rating on a continuous scale varying from 0 to 1, which can be either inferred from the intermediary of a category grading scale or obtained by direct measurement, and Nis apparent magnitude on a ratio scale, normalized to give N = 1 when t = 1/2 The value of the exponent k has not been precisely determined but it is believed to be close to unity. Where unrelated impairments are rated in terms of the same type of response, the scale of apparent magnitude closely approximates a scale of summable subjective magnitude.