A Single Scale Based on is Ratio and Partition Estimates
Miguelina Guirao Laboratorio de Investigaciones Sensoriales Consejo Nacional de Investigaciones Cientificas y Tecnicas, and Universidad de Buenos Aires
Ever since the pioneering work of Stevens and Galanter ( 1957), the issue of a nonlinear relation between category and ratio scales has been debated from many perspectives. The most frequently discussed are those related to judgmental bias and contextual effects (see reviews in Ward, 1973, and Poulton, 1989). Stevens and Galanter approached the problem mainly in terms of variability, which refers to the accuracy of subjective measurements of intensity levels. The amount of variability was taken as a criterion to distinguish intensive (prothetic) from nonintensive (metathetic) continua.
On intensive continua, since the size of the error increased with magnitude, the use of ratio scales seemed more appropriate. On nonintensive continua, the fact that the relative error tended to be constant over the continuum seemed to justify the use of partition scales. In the intervening years, several studies have found that the degree of nonlinearity observed between the two scales depends, among others factors, on the degree of variability ( Eisler, 1963; Stevens & Guirao, 1962). However, Stevens and Galanter were aware at the time of their 1957 paper that category scales approach linearity with magnitude estimations as the two numerical ranges become closer in size. Stevens and Guirao ( 1962) left the issue open when they wrote, "When the experimenter takes pains to choose procedures of sufficient inherent precision, the partition and the magnitude scales may become almost linearly related" (p. 1471).
The present work reexamines the form of the relation between the two