Academic journal article Attention, Perception and Psychophysics

Adaptive Psychophysical Methods for Nonmonotonic Psychometric Functions

Academic journal article Attention, Perception and Psychophysics

Adaptive Psychophysical Methods for Nonmonotonic Psychometric Functions

Article excerpt

Published online: 7 November 2013

© Psychonomic Society, Inc. 2013

Abstract Many psychophysical tasks in current use render nonmonotonic psychometric functions; these include the oddball task, the temporal generalization task, the binary synchrony judgment task, and other forms of the same- different task. Other tasks allow for ternary responses and render three psychometric functions, one of which is also nonmonotonic, like the ternary synchrony judgment task or the unforced choice task. In all of these cases, data are usually collected with the inefficient method of constant stimuli (MOCS), because extant adaptive methods are only applicable when the psychometric function is monotonic. This article develops stimulus placement criteria for adaptive methods designed for use with nonmonotonic psychometric functions or with ternary tasks. The methods are transformations of conventional up-down rules. Simulations under three alternative psychophysical tasks prove the validity of these methods, their superiority to MOCS, and the accuracy with which they recover direct estimates of the parameters determining the psychometric functions, as well as estimates of derived quantities such as the point of subjective equality or the difference limen. Practical recommendations and worked-out examples are provided to illustrate how to use these adaptive methods in empirical research.

Keywords Psychometrics . Testing . Signal detection theory

(ProQuest: ... denotes formulae omitted.)

Adaptive psychophysical methods have been designed for use with tasks in which the underlying psychometric function is monotone increasing, either from 0 to 1 (as in 2AFC discrimination tasks; see, e.g., Alcalá-Quintana & García-Pérez, 2011; Dyjas, Bausenhart, & Ulrich, 2012) or from 1/m to 1 (as in mAFC detection or log-increment detection tasks; see, e.g., Jäkel &Wichmann, 2006). The upper asymptote of the observed psychometric function may not be at unity because of lapses, but for simplicity, and without loss of generality, lapses will be leftaside in this description.1 With a monotone increasing psychometric function, the relevant stimulus range to probe is that within which the psychometric function exhibits nonasymptotic behavior, but the breadth and location of this range is not always known in advance. Adaptive methods locate this range and collect data there, using a placement criterion that decreases (or increases) the stimulus level when the observer's response suggests an upperasymptotic (or lower-asymptotic) regime. In some cases the psychometric function is instead monotone decreasing (see, e.g., Adams & Wakefield, 2009; Machilsen, Pauwels, & Wagemans, 2009; Machilsen & Wagemans, 2011), and conventional adaptive methods can still be used here with only reversing the stimulus placement criterion (i.e., increasing stimulus level when at the upper-asymptotic regime and decreasing it when at the lower-asymptotic regime).

But not all psychophysical tasks render monotonic psychometric functions, which makes conventional adaptive methods unusable unless the stimulus set is reduced to a subrange in which monotonic behavior occurs. For instance, in time perception, the so-called temporal generalization task (see, e.g., Wearden, 1992, 2008) requests on each trial that an observer responds whether the displayed duration is the same as or different from a standard duration presented at the beginning of the session. The psychometric function for this task has the inverted-U shape depicted in Fig. 1a, so that the probability of a "same" response decreases as the test duration departs from the standard duration in either direction. Also in time perception, the so-called synchrony judgment task presents in each trial a stimulus onset asynchrony (SOA, defined as the positive or negative delay between two stimuli), and the observer's task is to respond whether the two stimuli seemed to be presented synchronously or asynchronously (see, e. …

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