Issues in psychophysical measurement.
Two classes of ratio-scaling procedures are outlined—magnitude matching and ratio matching—and their assets and liabilities are noted. Partition-scaling procedures, which are supposedly designed for interval scaling, pro-duce results that can be described by a power function with a virtual or "as if " exponent. Since the virtual exponent is smaller than the actual exponent of the continuum, the category scale is nonlinear. The virtual exponent provides a convenient descriptor of several kinds of partition operations. Other topics discussed include individual differences among subjects ' exponents, procedures of averaging, and the effects of stimulus range on exponents. It is suggested that the power law asserts a nomothctic imperative. The task here is to review the matching procedures used to determine the power func-tions that govern the growth of sensation magnitude and to consider some of the sources of deviation and perturbation that have raised questions concerning the nomo-thetic quality of the psychophysical power law. Since all procedures of measurement in-volve matching operations, the interesting differences among different scales and differ-ent kinds of measurement can often be re-duced to a basic question: What was matched to what, and how? In the domain of psy-chophysics, numerous scaling methods have been invented, many of them useful for the determination of ratio scales of apparent magnitude. The approaches of ratio scaling can be catalogued in different ways, but for present purposes they fall into two general classes: magnitude matching, which includes the subclasses (a) cross-modality matching, ( b) magnitude estimation, and (c) magni-tude production; and ratio matching which includes the subclasses (a) cross-modal ra-tio matching, (6) ratio estimation, and (c) ratio production. Since there are endless variations on psy-chophysical procedures, it is possible here to