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.