Stevens’ Direct Scaling Methods and the Uniqueness Problem

Abstract

Direct scaling methods, ratio estimation, ratio production, uniqueness problem, scale types, axiomatic measurement theory,

What are we estimating when we fit Stevens’ power law?

“…Our approach could give even more precise predictions on the behavior of Stevens' exponent with more knowledge about the shape and forms of both ψ and W . This could come pursuing the line of research drawn in several recent experiments by Luce and Steingrimsson (Steingrimsson and Luce, 2005a, 2005b, 2006, 2007.…”

“…Therefore, as multiplicativity has been rejected in every domain in which it has been evaluated (loudness, brightness, contrast, perception of time, size of circles, and more), also W (1) = 1 has been rejected (as a general rule) empirically. Augustin (2006Augustin ( , 2010 presented theoretical extensions of Narens (2006) giving support to the fact that W (p) is either a power or a logarithmic function.…”

“…An important more recent achievement developed in this stream of literature includes the axiomatization of various novel theories which comprehend Stevens' model as a special case (Augustin, 2006(Augustin, , 2010Luce, 2002Luce, , 2008Narens, 1996Narens, , 2002Narens, , 2006. Following a terminology introduced by Luce (2002), we say formally that a psychological scale of subjective intensities can be represented in a separable form if there exist a psychophysical function ψ and a subjective weighting function W such that p is in the following relation with d 1 and d 2 :…”

Extensions of Narens' theory of ratio magnitude estimation

“…Then the following definition summarizes basic properties of ratio scaling that one would not expect to be violated empirically in an idealized setting (cf. Augustin, 2006):…”

“…The definition of a (restricted) direct scaling structure is due to Augustin (2006). It is important to note here that Axioms 1, 1′, 2, and 2′ (as well as Narens' original framework) refer to an idealized version of Stevens' direct scaling methods, in which a given stimulus configuration always elicits the same response, that is, there is no variability to be accomodated in the theory.…”