Human Psychophysical Functions, an Update: Methods for Identifying their form; Estimating their Parameters; and Evaluating the Effects of Important Predictors

Abstract

Stevens' power law for the judgments of sensation has a long history in psychology and is used in many psychophysical investigations of the effects of predictors such as group or condition. Stevens' formulation [Formula: see text], where [Formula: see text] is the psychological judgment, P is the physical intensity, and [Formula: see text] is the power law exponent, is usually tested by plotting log [Formula: see text] against log (P). In some, but by no means all, studies, effects on the scale parameter, [Formula: see text], are also investigated. This two-parameter model is simple but known to be flawed, for at least some modalities. Specifically, three-parameter functions that include a threshold parameter produce a better fit for many data sets. In addition, direct non-linear computation of power laws often fit better than regressions of log-transformed variables. However, such potentially flawed methods continue to be used because of assumptions that the approximations are "close enough" as to not to make any difference to the conclusions drawn (or possibly through ignorance the errors in these assumptions). We investigate two modalities in detail: duration and roughness. We show that a three-parameter power law is the best fitting of several plausible models. Comparison between this model and the prevalent two parameter version of Stevens' power law shows significant differences for the parameter estimates with at least medium effect sizes for duration.

Quality-Adjusted Life-Years without Constant Proportionality

“…The main contribution of this article is the set of 117 coefficient estimates (Tables 2 and 3) illustrating the relationship between life span, duration, and value on a QALY scale. The results suggest that respondents did not discount future events at a constant rate; instead, there appears to be a log-log relationship between time and value, similar to the power law in psychophysics [27,33].…”

The Indecision Model of Psychophysical Performance in Dual-Presentation Tasks: Parameter Estimation and Comparative Analysis of Response Formats

“…The form of μ has been under scrutiny for decades and it is still unclear whether a unique form exists (Kornbrot, 2016). Nevertheless, some aspects of the mathematical form of μ are immaterial in 2P tasks, where the values μ( x 1 ) and μ( x 2 ) at the stimulus levels x 1 and x 2 displayed first and second are not crucial and only their difference matters.…”

The Do’s and Don’ts of Psychophysical Methods for Interpretability of Psychometric Functions and Their Descriptors

“…The psychometric function is useful because its primary determinant is the psychophysical function , which expresses the mapping of some physical continuum onto the corresponding perceptual continuum (e.g., weight onto perceived heaviness or physical position onto perceived position). The psychophysical function could be measured directly with any of the classical psychophysical scaling methods (see, e.g., Kornbrot, 2016; Marks & Algom, 1998; Marks & Gescheider, 2002), but scaling faces many difficulties because humans do not naturally quantify perceived magnitude on a ratio scale. As Fechner (1860/1966, p. 47) put it, “the immediate judgment we can make in this context (…) is one of more or less, or one of equality, not one of how many times, which true measurement demands and which it is our purpose to derive”.…”