The normal distribution in scaling subjective stimulus differences: less "normal" than we think?

Abstract

The Gaussian, or "normal," distribution is routinely used to model distributions of subjective quantities. This practice rests on a trust in the central limit theorem, yet this theorem does not cover the case of a mixture of Gaussian distributions with different standard deviations, which yields a distribution that is heavier tailed than the Gaussian. In psychophysical judgment experiments, this may result, for example, from fluctuating or interindividually varying attention. Two candidates for describing this commonly encountered type of distribution are the logistic distribution and the t distribution with a small number of degrees of freedom. In reanalyses of experimental data on three-category loudness comparisons, as well as in a Monte Carlo simulation, t(4) was found to model the underlying mixed inter- and intraindividual distribution of subjective loudness differences quite satisfactorily.