How to define thresholds for level and interaural-level-difference discrimination: Insights from scedasticities and distributions

Abstract

Sensitivity to changes in the stimulus level at one or at both ears and to changes in the interaural level difference (ILD) between the two ears has been studied widely. Several different definitions of threshold and, for one of them, two different ways of averaging single-listener thresholds have been used (i.e., arithmetically and geometrically), but it is unclear which definition and which way of averaging is most suitable. Here, we addressed this issue by examining which of the differently defined thresholds yielded the highest degree of homoscedasticity (homogeneity of the variance). We also examined how closely the differently defined thresholds followed the normal distribution. We measured thresholds from a large number of human listeners as a function of stimulus duration in six experimental conditions, using an adaptive two-alternative forced-choice paradigm. Thresholds defined as the logarithm of the ratio of the intensities or amplitudes of the target and the reference stimulus (i.e., as the difference in their levels or ILDs; the most commonly used definition) were clearly heteroscedastic. Log-transformation of these latter thresholds, as sometimes performed, did not result in homoscedasticity. Thresholds defined as the logarithm of the Weber fraction for stimulus intensity and thresholds defined as the logarithm of the Weber fraction for stimulus amplitude (the most rarely used definition) were consistent with homoscedasticity, but the latter were closer to the ideal case. Thresholds defined as the logarithm of the Weber fraction for stimulus amplitude also followed the normal distribution most closely. The discrimination thresholds should therefore be expressed as the logarithm of the Weber fraction for stimulus amplitude and be averaged arithmetically across listeners. Other implications are discussed, and the obtained differences between the thresholds in different conditions are compared to the literature.

Keywords: Arithmetic statistics; Homoscedasticity; Interaural-level-difference discrimination; Level discrimination; Normal distribution; Threshold; Weber fraction.