Empirical evaluation of axioms fundamental to Stevens's ratio-scaling approach: I. Loudness production

Stevens's direct scaling methods rest on the assumption that subjects are c apable of reporting or producing ratios of sensation magnitudes. Only recen tly, however, did an axiomatization proposed by Narens (1996) specify neces sary conditions for this assumption that may be put to an empirical test. I n the present investigation, Narens's central axioms of commutativity and m ultiplicativity were evaluated by having subjects produce loudness ratios. It turned out that the adjustments were consistent with the commutativity c ondition; multiplicativity (the Bet that consecutive doubling and tripling of loudness should be equivalent to making the starting intensity six times as loud), however, was violated in a significant number of cases. Accordin g to Narens's (1996) axiomatization, this outcome implies that although in principle a ratio scale of loudness exists, the numbers used by subjects to describe sensation ratios may not be taken at face value.