Weight of evidence supports one operation for "ratios" and "differences" of heaviness

This paper investigates an apparent contradiction between recent studies of "ratios" and "differences" of heaviness. Birnbaum and Veit (1974) found a single rank order for judgments in the two tasks, whereas Rule, Curtis, and Mullin (1981), who used a different stimulus set, procedure, and experimental design, reported two orders. To investigate the cause of this discrepancy, the present study manipulated the experimental design using the same stimuli and procedure as Rule et al. (1981). In one experiment (within-subject designs), each subject judged all combinations of the standard and comparison stimulus; in the other experiment (between-subjects designs) each subject received only one standard, and different groups of subjects were given different standards. "Ratios" and "differences" of heaviness were monotonically related for the majority of subjects who judged all combinations of standards and comparisons. Variations in the modulus and response examples did not affect the rank order of "ratios" within subjects. These results suggest that the contradiction in results is due to the difference in experimental design rather than differences in stimuli or procedure. In the between-subjects designs, the rank order of the "ratio" judgments depended on the standards and examples. Both previous and present results are consistent with the theory that subjects use one operation, subtraction, for both tasks and that the judgment function varies with between-subjects manipulations of the standard, examples, and modulus.