Is a power function description of intensity-jnd data compatible with the loudness function?

A sequence of approximation for calculating loudness functions from the intensity-jnd function for a 1-kHz tone is performed. It is shown that a single power function representation of pure tone intensity-jnd data can generate a loudness function from a McGill-Goldberg type model in better agreement with loudness measurements than has heretofore been demonstrated. This improvement arises from the presence of an integration constant that had been previously ignored. The inclusion of the integration constant markedly improves the overall shape of the derived loudness function, somewhat more at low then at high intensity levels. Using the same near miss power function, the consequences of setting the integration constant equal to zero are indicated. These effects are compared to those obtained from the unaltered intensity-jnd data [W. S. Hellman and R. P. Hellman, J. Acoust. Soc. Am. Suppl. 1 82, S25 (1987)]. Corrections resulting from going beyond first order in the calculational procedure are discussed. [Partially supported by the Rehabilitation R&D Service of the VA.]