Octuplicate this interval! Axiomatic examination of the ratio properties of duration perception

The relationship between the physical intensity of a stimulus and its perceived magnitude can be described by Stevens' power law (Stevens, American Journal of Psychology, 69(1), 1-15, 1956), i.e., a power function with an exponent depending on the sensory modality studied. Direct scaling methods used to determine the power function exponent are based on the assumption that subjects are capable of processing ratios of magnitudes. The present experiments investigate whether this assumption holds for duration perception by empirically testing (Narens, Journal of Mathematical Psychology, 40(2), 109-129, 1996) fundamental axioms of monotonicity, commutativity, and multiplicativity. To determine whether the exponent can be interpreted in a meaningful way, i.e., whether it is invariant under changes of the reference stimulus, two further axioms, invertibility and weak multiplicativity (Augustin, Acta Psychologica, 128(1), 176-185, 2008) are evaluated. N=25 participants were required to adjust the duration of a comparison tone to specific ratios of different standard durations in two experiments. In accordance with previous findings for other sensory continua, monotonicity held for the duration adjustments of most participants. Significant violations of the commutativity axiom were found in 12.5% of all pertinent tests, whereas multiplicativity was violated in 32% of such tests. The axioms of weak multiplicativity and invertibility, however, were violated in over 50% of the tests. These results indicate that even though a ratio scale for perceived duration exists, the numbers as used by the participants cannot always be taken at face value and that even though power functions fit the data quite well, the exponent depends on the size of the standard and therefore cannot always be interpreted in a meaningful way.