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Lapsley Miller, J. A., Scurfield, B. K., Drga, V., Galvin, S. J., and
Whitmore, J.
Journal of Mathematical Psychology, 2002
46(4), 383-417
Abstract
Green’s relationship, ASI=P(C)2I, which equates
the area, ASI, under the receiver operating characteristic (ROC)
curve in the single-interval forced-choice (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 ASI and the
2IFC channel capacity, nonparametric bounds on the area under the2IFC ROC curve
in terms of ASI, 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. © Elsevier Science
Last updated
08 Nov 2009 04:37 PM
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