Ragnar Steingrimsson

Are psychophysical scales of intensities the same or different when stimuli vary on other dimensions? Theory with experiments varying loudness and pitch.

UNLABELLED Most studies concerning psychological measurement scales of intensive attributes have concluded that these scales are of ratio type and that the psychophysical function is closely approximated by a power function. Experiments show, for such cases, that a commutativity property must hold under either successive increases or successive decreases provided, e.g., all other independent dimensions are fixed. A good deal of data support this conclusion. However, little or no attention has been paid to whether or not such subjective intensity scales differ when an independent dimension such as frequency (pitch in audition, color in vision, etc.) is varied. Using a simple and favorably tested theoretical model for global psychophysics, the authors arrive at a necessary and sufficient cross-dimension, commutativity condition for a common intensity ratio scale to exist. For example, the data show that the loudness of a tone at frequency f and another tone at frequency g can each be viewed as arising from a common property of loudness over intensity/frequency pairs. Comparing one version of cross-dimensional commutativity with the corresponding 1-dimensional commutativity property discriminates between a general representation of the ratio scale property and a special case of it. FUTURE WORK Does the theory extend to other intensive continua (prothetic attributes)? If so, which ones? And does it extend to cross-modal matching?

Predictions from a Model of Global Psychophysics about Differences between Perceptual and Physical Matches

A well-known phenomenon is that “matched” successive signals do not result in physical identity. This phenomenon has mostly been studied in terms of how much the second of two signals varies from the first, which is called the time-order error (TOE). Here, theoretical predictions led us to study the more general question of how much the matching signal differs from the standard signal, independent of the position of the matching signal as the first or second in a presentation. This we call non-equal matches (NEM). Using Luce’s (Psychological Review, 109, 520–532, 2002, Psychological Review, 111, 446–454, 2004, Psychological Review, 115, 601, 2008, Psychological Review, 119, 373–387, 2012) global psychophysical theory, we predicted NEM when an intensity z is perceived to be “1 times a standard signal x.” The theory predicts two different types of individual behaviors for the NEM, and these predictions were evaluated and confirmed in an experiment. We showed that the traditional definition of TOE precludes the observation, and thus the study, of the NEM phenomenon, and that the NEM effect is substantial enough to alter conclusions based on data that it affects. Furthermore, we demonstrated that the custom of averaging data over individuals clearly leads to quite misleading results. An important parameter in this modeling is a reference point that plays a central role in creating variability in the data, so that the key to obtaining regular data from respondents is to stabilize the reference point.

Evolutionary Game Theoretical Model Of The Evolution Of The Concept Of Hue, A Hue Structure, And Color Categorization In Novice And Stable Learners

Evolutionary game theory is used to form a finite partition of a continuous hue circle in which perceptually similar hues are each represented by an icon chip and the circle by a finite but game dynamically determined number of icon chips. On the basis of such icon chip structures, a color categorization for both an individual learner and a population of learners is then evolved. These results remove limitations of some particular previous color categorization simulation work which assumed a fixed number of color stimuli and a maximal number of predefined color categories. These simulations are extended to demonstrate that learners need neither to share the same icon chip structures, nor do these structures have to be fully developed for a population of learners to produce a stable color categorization system. Additionally, when a naive learner is introduced into a population with a stable color categorization, the game dynamics result in the learners adopting the existing categorization. All results are shown to hold while the underlying icon chip structures evolve continuously in response to novel stimuli. The usefulness of the approach as well as some of the potential implications of the results for human learning of color categories are discussed.