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

The parameters in the near-miss-to-Weber's law

“…It is noteworthy that these predictions are consistent with empirical findings: Doble et al (2006) showed that Eq. (19) with a decreasing parameter function p7 !bðpÞ provides a good fit to pure tone intensity discrimination data.…”

“…Falmagne (1994) showed that, under certain side conditions, the exponent bðpÞ is either a real valued constant b or an exponential function of the type bðpÞ ¼ y expðgF À1 ðpÞÞ (Falmagne, 1994, Theorem 3). A recent paper by Doble, Falmagne, Berg, and Southworth (2006) on psychoacoustics provides empirical evidence that bðpÞ is a decreasing function of the criterion p. Furthermore, the data indicate that the two parameters bðpÞ and KðpÞ are related by a simple relationship of the form…”

“…Furthermore, Doble et al (2006) emphasize the following fixed point property of Eq. (8): For any criterion value p, and any intensity a, ln x p ðaÞ a ¼ lnðÞ À bðpÞ lnðdÞ þ ðbðpÞ À 1Þ lnðaÞ…”

“…(8) as fixedpoint-model. Doble et al (2006) argue that Eq. (9) is in accordance with the idea of a high-level fixed point which is used in the subjective evaluations of the intensities of acoustical stimuli.…”

A generalization of Piéron's law to include background intensity and latency distribution

“…The relevant experimental work on the intensity discrimination of pure tones was recently reported by Doble, Falmagne, and Berg (2004), where they clearly showed that the exponent in the homogeneity equation is not a constant but a function of the discrimination criterion.…”