Comparing Time-Accuracy Curves: Beyond Goodness-of-Fit Measures

By Liu, Charles C.; Smith, Philip L. | Psychonomic Bulletin & Review, February 2009 | Go to article overview

Comparing Time-Accuracy Curves: Beyond Goodness-of-Fit Measures


Liu, Charles C., Smith, Philip L., Psychonomic Bulletin & Review


The speed-accuracy trade-off (SAT) is a ubiquitous phenomenon in experimental psychology. One popular strategy for controlling SAT is to use the response signal paradigm. This paradigm produces time-accuracy curves (or SAT functions), which can be compared across different experimental conditions. The typical approach to analyzing time-accuracy curves involves the comparison of goodness-of-fit measures (e.g., adjusted-R^sup 2^), as well as interpretation of point estimates. In this article, we examine the implications of this approach and discuss a number of alternative methods that have been successfully applied in the cognitive modeling literature. These methods include model selection criteria (the Akaike information criterion and the Bayesian information criterion) and interval estimation procedures (bootstrap and Bayesian). We demonstrate the utility of these methods with a hypothetical data set.

(ProQuest: ... denotes formulae omitted.)

Response time (RT) and response accuracy are the two most common dependent variables in experimental psychology. These two variables are often measured together to assess the possibility of a speed-accuracy trade-off (SAT): That is, at a given level of sensitivity, faster responses tend to produce more errors. The SAT phenomenon is often unrelated to the underlying mental processes of interest and, therefore, has been regarded as a nuisance variable in most studies.

One strategy for controlling SAT is to formulate a quantitative model for the decision process. For example, sequential sampling models of decision making account for SAT with a criterion parameter, which determines the amount of information accumulated by the participant before he or she responds (Link, 1992; Ratcliff & P. L. Smith, 2004; P. L. Smith, 2000). This criterion parameter can be estimated simultaneously with other parameters, including those that index the strength and variability of underlying representations. However, full specification of a sequential sampling model requires a number of detailed, and often highly technical, assumptions about the model architecture, and the models are usually fitted to entire distributions of both correct and error RTs. It is not surprising, then, that routine application of sequential sampling modeling is rare in experimental psychology.1 Here, we will focus on an alternative, and more popular, method known as the response signal paradigm.

Response Signal Paradigm

The response signal paradigm is a popular method for controlling SATs (Dosher, 1979; Reed, 1976; Wickelgren, 1977). This method allows the effects of discriminability to be decoupled from those of criterion shifts, because the experimenter specifies the time at which a response must be made. On each trial, observers are instructed to respond as soon as they hear a response signal (an auditory tone), which is presented at one of several deadline lags. At early lags, the observer often responds at close to chance, because there is not enough time to fully integrate the available information. As lag increases, accuracy improves monotonically to an asymptote. This time-accuracy curve is often referred to as the SAT function.

When accuracy is measured in d' units, the data are usually fitted by a three-parameter shifted exponential function:

... (1)

where λ is the asymptotic accuracy, 1/β is the rate at which accuracy approaches the asymptote from chance (d' = 0), and d is the time at which accuracy begins to exceed chance.

The response signal paradigm allows us to characterize the effect of experimental manipulations across the entire time course of decision processing. One of the primary reasons for using this paradigm is to compare estimates of processing dynamics across conditions in which asymptotic accuracy varies. In principle, observed differences between conditions may be due to changes in one or more parameters of the shifted exponential function. …

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