Nonparametric Relationships between Single-Interval and Two-Interval Forced-Choice Tasks in the Theory of Signal Detectability

Abstract

Green's relationship, A SI =P(C) 2I , which equates the area, A SI , under the receiver operating characteristic (ROC) curve in the single-interval forcedchoice (SIFC) task with the proportion correct, P(C) 2I , in the two-interval forced-choice (2IFC) task, is rederived using the cross-correlation functions of the SIFC evidence distributions. The relationship is generalized to include discrete random variables, unidimensional decision axes that do not need to be monotonic with likelihood ratio, and arbitrary prior and guessing probabilities. A 2IFC difference decision rule is assumed. Further nonparametric relationships, including an equality between an entropy transform of A SI and the 2IFC channel capacity, nonparametric bounds on the area under the 2IFC ROC curve in terms of A SI , and methods for estimating 2IFC ROC curves based on information from the SIFC task, are developed. These relationships are investigated experimentally. Experiment I is a frequency-discrimination task where the evidence is known to be distributed as a discrete random variable. Experiment II is an amplitude-discrimination task where the theoretical evidence distributions are continuously distributed. The problem of observer inconsistency is addressed by repeating the experiments multiple times, using the same stimuli, then using group operating characteristic (GOC) analysis to remove unique noise. Results from Experiment I show excellent support for all the theoretical relationships, and results from Experiment II show partial support for the theoretical relationships.

The effects of noise-bandwidth, noise-fringe duration, and temporal signal location on the binaural masking-level difference

“…Frozen noise presentation (compared to the presentation of independent noise samples) in each observation interval may to some extent reduce effects of sampling variability (a component of which may be composed of internal noise). Further understanding of the contribution of internal noise to detection tasks may be achieved by applying other techniques such as estimating consistency of auditory judgments (Green, 1964) and decision-fusion (Taylor et al, 1991;Lapsley Miller et al, 2002).…”

The role of the bandwidth-duration product WT in the detectability of diotic signals

“…The GOC curve and the mROC curve for all observers, and the theoretical ROC curve in the SIFC condition in Experiment I (from Lapsley Miller et al (1999) An example of a FORA fitted to the empirical FORA using the method described by Drga (1999)…”

“…1 Both have been used as a basis for theories about the detectability of many types of acoustic stimuli, and there are a number of theoretical relationships linking the two tasks. For instance, Lapsley Miller, Scurfield, Drga, Galvin, and Whitmore (1999) and Scurfield (1995Scurfield ( , 1996 have examined and extended the non-parametric relationships between the SIFC and 2IFC tasks, both theoretically and experimentally. One of their conclusions was that the SIFC task is often preferable to the 2IFC task.…”

“…The non-parametric relationship that equates the area, A SIFC , under the receiver operating characteristic (ROC) curve in the SIFC task to the proportion of correct decisions, P(C) 2IFC , in the 2IFC task (Green, 1964b;Green & Moses, 1966;Green & Swets, 1966). Lapsley Miller et al (1999) extended this relationship, by removing unnecessary assumptions about how the evidence is distributed, by generalising to discrete random variables, and considering evidence distributed over the x decision axis and not just the likelihood ratio decision axis `(x).…”

“…3. Scurfield's (Lapsley Miller et al, 1999;Scurfield, 1995Scurfield, , 1996 new measures of detectability: D SIFC and C 2IFC . 4.…”