Judgments of differences and ratios of numerals

Each subject performed two tasks, dividing a line segment so that either (a) the ratio of subjective lengths corresponded to the ratio of the magnitudes of two numerals or (b) the difference in length was proportional to the numerical difference. Had subjects actually performed two operations on the same scale, the responses would have been nonmonotonically related. Instead, data for the two tasks were nearly identical and ordinally compatible with either a ratio or a subtractive model. The ratio model implied scale values for numerals that were a positively accelerated function of numerical value, inconsistent with previous results. With a nonlinear response function for gl:aphic length, the subtractive model fit well, yielding scale values that were a negatively accelerated function of numerical value and a linear function of previously obtained scales. These results, together with other recent findings, suggest that subjects may perform the same operation in spite of instructions to judge "ratios" or "differences" and that this operation can be best represented by a subtractive model.