Quantifying private events: A functional measurement analysis of equisection

Functional measurement theory was applied to bisection, trisection, and quadrisection of grayness. Theoretically, these judgments should obey an averaging model. But the overt responses are not a valid measure of subjective magnitude (since they are made on the physical stimulus continuum), and so they cannot be used directly to test the model. However, scaling and model testing can both be accomplished simultaneously using functional measurement theory. If the subject is indeed averaging, then there exists a monotone transformation that makes the data additive; and this transformation can be computed with FUNPOT, Weiss’s (1973a) computer program which finds polynomial transformations that reduce selected effects. Further, determination of this transformation also reveals the psychophysical function, because it gives the relation between subjective magnitude and overt response. For bisection, the averaging model was successful; it was possible to find a monotone transformation that made the data additive. This psychophysical function differed somewhat in form from the Munsell scale. It gained cross-task validity from its agreement with a grayness scale obtained from rating data (Weiss, 1972). For trisection and quadrisection, the averaging model was not accepted; it was not possible consistently to find transformations which induced additivity.