Systematic covariation of the parameters in the near-miss to Weber's law, pointing to a new law

The exponent in the power function modeling of the near-miss to Weber's law is known to depend on several experimental factors, such as tone frequency and the presence or absence of noise. This paper presents data that confirm a theoretical argument that the near-miss exponent also depends on the definition of ‘just-noticeably different’ used empirically. Intensity discrimination data were collected for pure, 1000-Hz tones presented in quiet. Referent sound pressure levels ranged from 40 to 80 dB SPL in 10-dB steps. For each referent, the tone judged louder than the referent with probability equal to ν was determined, with ν ranging from 0.16 to 0.84. It was found that the power function exponent decreases monotonically with ν. Moreover, it was found that the two power law parameters co-vary systematically with ν, implying a submodel that has an interesting fixed-point property.     

A threshold theory account of psychometric functions with response confidence under the balance condition

The study of thresholds for discriminability has been of long‐standing interest in psychophysics. While threshold theories embrace the concept of discrete‐state thresholds, signal detection theory discounts such a concept. In this paper we concern ourselves with the concept of thresholds from the discrete‐state modelling viewpoint. In doing so, we find it necessary to clarify some fundamental issues germane to the psychometric function (PF), which is customarily constructed using psychophysical methods with a binary‐response format. We challenge this response format and argue that response confidence also plays an important role in the construction of PFs, and thus should have some impact on threshold estimation. We motivate the discussion by adopting a three‐state threshold theory for response confidence proposed by Krantz (1969, Psychol. Rev., 76, 308–324), which is a modification of Luce's (1963, Psychol. Rev., 70, 61–79) low‐threshold theory. In particular, we discuss the case in which the practice of averaging over order (or position) is enforced in data collection. Finally, we illustrate the fit of the Luce–Krantz model to data from a line‐discrimination task with response confidence.     

Recasting (the near-miss to) Weber's law

The authors argue mathematically that a common, power-function model of the just-noticeable difference in stimulus intensities is logically inconsistent with an exponent other than 1 in those frequent situations in which a particular averaging over experimental conditions has taken place. The authors show that an alternative power-law model, one which does not share this logical inconsistency, provides a good fit to many well-known, psychoacoustic intensity discrimination data. They also show that the exponent in this alternative model must be nonconstant with the discrimination criterion in experiments implementing this averaging of data.