The optimum decision rules for the oddity task

Abstract

This paper presents the optimum decision rule for an m-interval oddity task in which m -1 intervals contain the same signal and one is different or odd. The optimum decision rule depends on the degree of correlation among observations. The present approach unifies the different strategies that occur with "roved" or "fixed" experiments (Macmillan & Creelman, 1991, p. 147). It is shown that the commonly used decision rule for an m-interval oddity task corresponds to the special case of highly correlated observations. However, as is also true for the same-different paradigm, there exists a different optimum decision rule when the observations are independent. The relation between the probability of a correct response and d' is derived for the three-interval oddity task. Tables are presented of this relation for the three-, four-, and five-interval oddity task. Finally, an experimental method is proposed that allows one to determine the decision rule used by the observer in an oddity experiment.The oddity task provides a means of measuring the observer's ability to discriminate between different stimuli.In the most general form, m stimuli are presented on each trial and there are m response alternatives. Despite the number ofresponse alternatives, there are actually only two stimuli. On any single trial, m -1 ofthe stimuli are the same; only one stimulus is different, the odd stimulus. The observer's task is to select the alternative with the odd stimulus. A frequent argument given for the use of this procedure is that it does not force the observer to distinguish between the two stimuli on some predetermined sensory dimension; rather, it offers the observer the freedom to make the distinction on whatever basis is most convenient. Therefore, when the stimuli are complex-as is often the case in, for example, food research-the oddity task is frequently used to assess the subject's ability to discriminate between different food alternatives.Forced-choice paradigms differ in the degree and extent to which the specific stimulus alternatives must be labeled or categorized. Without prior knowledge of the stimulus alternatives, it is often difficult to label the stimuli without considerable practice and training. It may even be impossible if the stimuli are not fixed, but vary over trials. To take a concrete example, suppose the task is to select from a pair of sinusoids the one with the higher pitch. One sound has frequency I: S], whereas the other sound has frequency j+ Sf. Let us calljthe standard frequency. In a one-interval, forced-choice paradigm, a single sinusoid isThe authors gratefully acknowledge Todd Maddox, Sandy MacRae, and an anonymous reviewer for their valuable comments, and for their suggestions for improving the readability of the manuscript. Correspondence should be addressed to N. 1. Versfeld, TNO

Evidence of across-channel processing for spectral-ripple discrimination in cochlear implant listeners

“…More specifically, for the fixed-phase condition, in which the "odd" stimulus always had p/2 starting phase, the test is a threeinterval, three-alternative forced-choice task. For the random-phase condition, in which the starting phase of the "odd" stimulus varies across trials, the test is a three-interval oddity task (Versfeld et al, 1996). Subjects were asked to click on an onscreen button that was labeled 1, 2, and 3 after they were presented the stimuli.…”

A Thurstonian model for the dual pair (4IAX) discrimination method

“…Such proportions allow for the determination of the unbiased measure of sensitivity d ¢. Other models, like that developed by Versfeld, Dai, and Green (1996) for the triangle/3-interval oddity task, cannot take response bias into account and make the assumption that the observer is unbiased. This is also the assumption made in the tables developed by D. M. Ennis (1993) and J. P. Ennis, D. M. Ennis, Yip, and O'Mahony (1998).…”

“…The differencing strategy has been described as nonoptimal compared with the alternative strategy (Macmillan et al, 1977), since the subject's performance would be lower. The conditions for using the two strategies have been reported to depend on the complexity of the stimuli (Irwin & Francis, 1995) and on the roving or fixed design of stimulus presentation Macmillan & Creelman, 1991;Versfeld et al, 1996). For further discussion about this issue, see Rousseau (2001).…”

A general formula for computing maximum proportion correct scores in various psychophysical paradigms with arbitrary probability distributions of stimulus observations

“…The formula is consistent with fundamental principles of statistical decision theory and, more specifically, with basic model of psychophysical SDT (Green & Swets, 1966). Using this model, optimal (ML) decision strategies for the various paradigms have been analyzed in earlier publications, almost invariably assuming Gaussiandistributed sensory observations (e.g., Dai & Kidd, 2009;Dai & Micheyl, 2010, 2012Dai, Versfeld, & Green, 1996;Green & Dai, 1991;Green & Swets, 1966;Irwin & Hautus, 1997;Irwin, Hautus, & Butcher, 1999;Macmillan & Creelman, 2005;Micheyl & Dai, 2008Micheyl & Messing, 2006;Noreen, 1981;Rousseau & Ennis, 2001, 2002Versfeld, Dai, & Green, 1996). Readers who are interested in details are referred to these earlier publications.…”