Notes and commentHow to measure post-error slowing: A confound and a simple solution
Highlights
► We show that the traditional measure of post-error slowing can be confounded. ► We illustrate this confound with both simulations and real data. ► We offer a solution that is both simple and adequate.
Introduction
People tend to slow down after they commit an error, a phenomenon known as post-error slowing (PES). Ever since the classic article “What does a man do after he makes an error?” (Rabbitt, 1966), the PES phenomenon has received considerable attention in the response time (RT) literature and several explanations have been proposed to explain its existence (e.g, Laming, 1968, Laming, 1979, Notebaert et al., 2009, Rabbitt & Rodgers, 1977, see Dutilh, Vandekerckhove, Forstmann, & Wagenmakers, 2012), for an empirical comparison). The most popular account of PES states that it reflects an error-induced increase in response caution that allows a participant to maintain a relatively constant level of accuracy (e.g., Botvinick, Braver, Barch, Carter, & Cohen, 2001, Smith & Brewer, 1995).
Specifically, this account holds that participants continually monitor their performance and interpret errors as a sign that the chosen response threshold was too liberal. Consequently, participants heighten their threshold following an error in order to increase the probability of a correct response on the next trial. The heightened threshold leads to fewer errors but also causes slower responding (i.e., the PES phenomenon).
At the same time, participants interpret correct responses as a sign that the chosen response threshold was too conservative, and therefore they are assumed to lower their threshold following each correct response. Thus, participants become more cautious after an error and slightly more daring after a correct response; in this way the system self-regulates to a state of homeostasis characterized by fast responses and few errors. Fig. 1, based on fictitious but representative data, illustrates the typical pattern of modest post-correct speed-up and pronounced post-error slowing (e.g., Brewer and Smith, 1989, Smith and Brewer, 1995).
This response-monitoring interpretation of PES suggests that the amplitude of PES can be used as a direct measure of cognitive control.1 Although the response monitoring/cognitive control interpretation might not be appropriate in all cases (e.g., Dutilh, Forstmann, Vandekerckhove, & Wagenmakers, submitted for publication, Notebaert et al., 2009), in many studies it is assumed to be correct from the outset. Consequently, the magnitude of PES is often treated as an important dependent variable that is correlated with neurophysiological variables such as anterior cingulate activity (Danielmeier et al., 2011, Li et al., 2006), error-related negativity (ERN) and positivity (Pe; Hajcak, McDonald, & Simons, 2003b), and cortisol levels (e.g., Tops & Boksem, 2010).
In this article we discuss how PES can best be measured. First we explain how, although straightforward and intuitive, the traditional method to quantify PES can create spurious PES or mask real PES as a result of global changes in performance. We illustrate this confound with two simulation studies and then show how the confound can be eliminated. The final section illustrates both spurious and masked PES in a real data set.
Section snippets
The measurement of post-error slowing
There are several methods to quantify PES. The most insightful method plots the fluctuations in mean RT surrounding an error (e.g., Brewer and Smith, 1989, Smith and Brewer, 1995; see Fig. 1 for an example). The resulting graph shows mean RT for error trial , mean RT for subsequent trials , etc., and mean RT for preceding trials , etc. The form of the graph depends slightly on what trials are included in the calculations. For example, one may choose to include pre-error trials
A confound
The traditional method of quantifying PES, , has strong face validity. However, the method is vulnerable to a confound that was already hinted at by Laming (1979, p. 205) when he suggested …
…the possibility that errors and the increased RT on trials which follow them are jointly due to a local deterioration in performance. Suppose, for example, that the subject suffers short periods of relative inattention to the CR [choice response] task …During
Simulation studies
In two simulation studies we used the diffusion model (Ratcliff, 1978, Ratcliff and McKoon, 2008, Wagenmakers, 2009) to make the scenarios described above more concrete. The diffusion model produces both RTs and percentage correct. Most importantly for this study, the model can describe the specific influences of motivation and response caution on response time data.
A simple solution
The above confounds arise because post-correct and post-error trials (i.e., the trials used to calculate ) are not evenly distributed across the time series. The confounds can be eliminated when we compare post-error trials to post-correct trials that originate from the same locations in the time series. One natural option is to use post-correct trials that are pre-error trials at the same time. So, instead of comparing the mean RTs of all post-error trials to those of all
Towards a principled solution
The measure is designed to be immune against global performance fluctuations that may adversely affect the widely used measure . However, two important problems remain. First, PES measures capture error-induced changes in a specific variable, namely mean RT; the measures ignore changes in accuracy and changes in RT distributions. Such changes can be captured by the diffusion model described above. The diffusion model, however, currently does not have a mechanism for
Empirical Illustration: the confound is real
The simulations above showed that can detect spurious PES and mask real PES. We now provide an empirical illustration of these two situations. For this illustration, we selected data from two individual participants from a larger study that will be published elsewhere.
Concluding comments
Over the last two decades, cognitive control has become a major research topic in experimental psychology. PES is assumed to be an indicator of cognitive control and as such it is often used as an important behavioral variable. Recently, however, some studies have questioned whether PES really reflects cognitive control (e.g., Dutilh et al., 2012, Notebaert et al., 2009). In this study, however, we focused on a more elementary issue regarding the application of PES as a dependent variable: the
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