Abstracts Psychology

Evaluating the Ratio Scalability of Perceived DurationAn Axiomatic Study

by Jana Birkenbusch

The relationship between the physical intensity t of a stimulus and its perceived magnitude φ(t) can be described by Stevens’ power law φ(t) = αt^β (Stevens, 1956). The exponent of the power function β, crucial for the shape of the psychophysical function, depends on the sensory modality studied and can be estimated via direct scaling experiments. As recent developments in axiomatic measurement theory have shown, the application of direct scaling is based on fundamental assumptions concerning the participants’ scaling behavior: The observers’ perception of the investigated modality needs to be ordered on a sensory continuum and has to be valid on a ratio scale. Furthermore, the numbers as presented in the experimental instructions have to be processed as exact mathematical values. Narens (1996) made these implicit assumptions empirically testable by expressing them in the behavioral axioms of monotonicity, commutativity and multiplicativity. However, rigorous axiomatic testing showed that most participants fail to veridically process the numerical instructions used in production or estimation tasks. Steingrimsson and Luce (2007) have thoroughly analyzed the kind of “numerical distortion” that appears to be operating and claimed that the relationship between perceived and mathematical numbers can be described by a power function. To make this assumption empirically testable, they formulated the axiom of k-multiplicativity. The present thesis aimed to empirically evaluate this axiomatic framework to the perception of short durations. This was accomplished by combining axiomatic testing strategies derived from different theoretical approaches (Augustin, 2008; Narens, 1996; Steingrimsson & Luce, 2007) in a single reinvestigation thereby affording a much more precise determination of the concept of ratio scalability than in the most earlier empirical studies. Furthermore, the application domain was human time perception, which had not been subjected to this kind of axiomatic approach before. The aim of Manuscript A (N = 25) was to find out whether the basic assumptions for the application of direct scaling methods are valid for the perception of short durations. Furthermore it was tested whether the estimated power law parameters are invariant under changes of the reference stimulus and thus psychologically relevant. 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 were violated in over 50% of the tests, indicating a problem with psychological relevance. Manuscript B examined whether a relationship between mathematical and perceived numbers can be described by a power function with a constant exponent and whether there is a difference between the processing of integers and fractions. To that effect, the validity of k-multiplicativity… Advisors/Committee Members: Ellermeier, Wolfgang (advisor), Heller, Jürgen (advisor).