How functional measurement can yield validated interval scales of mental quantities

Abstract

Functional measurement provides simple methods for measuring mental quantities on equal-interval scales. The essential logic of functional measurement is illustrated for the linear model, which might apply to product attractiveness, and for the multiplying model, which might apply to work performance. These algebraic models are viewed as mathematical functions that determine how the stimulus cues are integrated into a unitary judgment. The logic of functional measurement rests on using these integration functions as the base and frame for psychological measurement. If factorial design can be used, then the analyses may require no more than a graph of the raw data. Functional measurement is compared to magnitude estimation and to paired-comparison scaling, and various methodological problems are discussed. Eight experiments on algebraic models are summarized to illustrate and give empirical support to the functional measurement approach. These experiments are part of an extensive research program that indicates that much of human judgment follows a general cognitive algebra. (55 ref) (PsycInfo Database Record (c) 2025 APA, all rights reserved)