Academic journal article Psychonomic Bulletin & Review

Psychological Interpretation of the Ex-Gaussian and Shifted Wald Parameters: A Diffusion Model Analysis

Academic journal article Psychonomic Bulletin & Review

Psychological Interpretation of the Ex-Gaussian and Shifted Wald Parameters: A Diffusion Model Analysis

Article excerpt

A growing number of researchers use descriptive distributions such as the ex-Gaussian and the shifted Wald to summarize response time data for speeded two-choice tasks. Some of these researchers also assume that the parameters of these distributions uniquely correspond to specific cognitive processes. We studied the validity of this cognitive interpretation by relating the parameters of the ex-Gaussian and shifted Wald distributions to those of the Ratcliff diffusion model, a successful model whose parameters have well-established cognitive interpretations. In a simulation study, we fitted the ex-Gaussian and shifted Wald distributions to data generated from the diffusion model by systematically varying its parameters across a wide range of plausible values. In an empirical study, the two descriptive distributions were fitted to published data that featured manipulations of task difficulty, response caution, and a priori bias. The results clearly demonstrate that the ex-Gaussian and shifted Wald parameters do not correspond uniquely to parameters of the diffusion model. We conclude that researchers should resist the temptation to interpret changes in the ex-Gaussian and shifted Wald parameters in terms of cognitive processes. Supporting materials may be downloaded from http://pbr.psychonomic-journals.org/content/supplemental.

(ProQuest: ... denotes formulae omitted.)

The analysis of response times (RTs) has a long history in cognitive psychology (e.g., Hohle, 1965; Luce, 1986; Ratcliff & McKoon, 2008; Townsend & Ashby, 1983). To draw inferences about mental processes, researchers originally relied on measures of central tendency such as the mean or median RT. As it became clear that these measures may lose important information (e.g., Heathcote, Popiel, & Mewhort, 1991), a growing number of researchers started to use mathematical and statistical models that can accommodate not just mean RT, but also the shapes of entire RT distributions.

Primary among the statistical models that facilitate the analysis of RT distributions are the ex-Gaussian and the shifted Wald. Changes in the parameters of these distributions may be used to summarize the effects of experimental manipulations. For instance, Leth-Steensen, King Elbaz, and Douglas (2000) found that children with ADHD differed from age-matched controls specifically in the ex-Gaussian parameter that captures the tail of the RT distribution.

Although the ex-Gaussian and shifted Wald distributions are sometimes used as purely descriptive tools (see, e.g., Wagenmakers, van der Maas, Dolan, & Grasman, 2008), many researchers go one step farther and assume that changes in the parameters of these distributions map onto changes in specific cognitive processes. For instance, Kieffaber et al. (2006) argued that changes in the Gaussian component of the ex-Gaussian distribution reflect changes in attentional cognitive processes, whereas changes in the exponential component reflect changes in intentional cognitive processes. The purpose of our study is to examine whether this mapping from parameters to processes is warranted. To this end, we attempt to link the parameters of the descriptive distributions to those of the Ratcliff diffusion model (Ratcliff, 1978). The diffusion model provides a theoretical account of performance in speeded two-choice tasks and has been successfully applied across a wide range of paradigms. Most importantly, the parameters of the diffusion model correspond to well-defined psychological processes, such as the rate of information accumulation (influenced by task difficulty or participant ability), response caution, a priori bias, and the time taken by processes unrelated to decision making (e.g., encoding and motor processes). The association between the diffusion model parameters and the psychological processes they are supposed to represent has been confirmed in numerous experiments (e.g., Voss, Rothermund, & Voss, 2004; Wagenmakers, Ratcliff, Gomez, & McKoon, 2008). …

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