Multidimensional Fechnerian Scaling: Basics

Fechnerian scaling is a theory of how a certain (Fechnerian) metric can be computed in a continuous stimulus space of arbitrary dimensionality from the shapes of psychometric (discrimination probability) functions taken in small vicinities of stimuli at which these functions reach their minima. This theory is rigorously derived in this paper from three assumptions about psychometric functions: (1) that they are continuous and have single minima around which they increase in all directions; (2) that any two stimulus differences from these minimum points that correspond to equal rises in discrimination probabilities are comeasurable in the small (i.e., asymptotically proportional), with a continuous coefficient of proportionality; and (3) that oppositely directed stimulus differences from a minimum point that correspond to equal rises in discrimination probabilities are equal in the small. A Fechnerian metric derived from these assumptions is an internal (or generalized Finsler) metric whose indicatrices are asymptotically similar to the horizontal cross-sections of the psychometric functions made just above their minima. Copyright 2001 Academic Press.     

Anecdotal, Statistical, and Causal Evidence: Their Perceived and Actual Persuasiveness

Claims about the occurrence of future events play an important role in pragmatic argumentation. Such claims can be supported by inductive arguments employing anecdotal, statistical, or causal evidence. In an experiment, the actual and perceived persuasiveness of these three types of evidence were assessed. A total of 324 participants read a newspaper article in which it was claimed that the building of a cultural centre would be profitable. This claim was supported by either anecdotal, statistical or causal evidence. The statistical evidence proved to be more convincing than the anecdotal and causal evidence. Although the latter two evidence types were equally unconvincing, the anecdotal evidence was perceived as less persuasive than the causal evidence. Therefore, the actual and perceived persuasiveness of the evidence did not correspond. These results partly replicate the results obtained in previous experiments. They also underscore the need to distinguish between the perceived and the actual persuasiveness of an argument.     

Modeling spatial effects in visualtactile saccadic reaction time

Saccadic reaction time (SRT) to visual targets tends to be shorter when nonvisual stimuli are presented in close temporal or spatial proximity, even when subjects are instructed to ignore the accessory input. Here, we investigate visualtactile interaction effects on SRT under varying spatial configurations. SRT to bimodal stimuli was reduced by up to 30 msec, in comparison with responses to unimodal visual targets. In contrast to previous findings, the amount of multisensory facilitation did not decrease with increases in the physical distance between the target and the nontarget but depended on (1) whether the target and the nontarget were presented in the same hemifield (ipsilateral) or in different hemifields (contralateral), (2) the eccentricity of the stimuli, and (3) the frequency of the vibrotactile nontarget. The time-window-of-integration (TWIN) model for SRT (Colonius & Diederich, 2004) is shown to yield an explicit characterization of the observed multisensory spatial interaction effects through the removal of the peripheral-processing effects of stimulus location and tactile frequency.     

Dissimilarity cumulation theory and subjective metrics

We present a new mathematical notion, dissimilarity function, and based on it, a radical extension of Fechnerian Scaling, a theory dealing with the computation of subjective distances from pairwise discrimination probabilities. The new theory is applicable to all possible stimulus spaces subject to the following two assumptions: (A) that discrimination probabilities satisfy the Regular Minimality law and (B) that the canonical psychometric increments of the first and second kind are dissimilarity functions. A dissimilarity function Dab for pairs of stimuli in a canonical representation is defined by the following properties: (1) a≠b?Dab>0; (2) Daa=0; (3) If and , then ; and (4) for any sequence {a_nX_nb_n}_n∈N, where X_n is a chain of stimuli, Da_nX_nb_n→0?Da_nb_n→0. The expression DaXb refers to the dissimilarity value cumulated along successive links of the chain aXb. The subjective (Fechnerian) distance between a and b is defined as the infimum of DaXb+DbYa across all possible chains X and Y inserted between a and b.     

Die Bedeutung von “Figur” und “Grund” für bie unveränderter Schwarzinduktion bestimmte Helligkeitsschwellen

Ohne Zusammenfassung