Internal Consistency in Event-Related Potentials associated with the Eriksen Flanker Experiment

In the present psychiatric literature, average Event-Related Potentials (ERPs) are often linked to psychiatric disorders. After awareness of making an error, the brain will react. Average ERPs are derived by averaging these brain reactions over all errors. However, if only a few errors are available, the average ERP can be unreliable. Recent studies show attention for examining the reliability of ERPs. These studies try to find the number of errors that makes ERPs reliable, or, internal consistent. Olvet and Hajcak (2009), Marco-Pallares et al. (2011), Pontifex et al. (2010), Meyer et al. (2013), Rietdijk et al. (2014) use Cronbach's α to measure internal consistency. However, this gives two problems. First, of all errors made by a participant, only some errors are used to obtain α, while taking another set of errors could give another value for α. Secondly, one of the main assumptions underlying Cronbach's α is violated. This assumption states that precisely the same trials need to be used over participants. Nevertheless, it is quite unlikely that participants fail exactly the same trials. The main goal of this research is to investigate whether these problems bias the number of errors that these studies find. Furthermore, having reliable average ERPs depends on whether brain activity is independent of error trials. Therefore, another goal is to justify averaging over all error trials, that is, to show independency of brain activity over error trials. To meet the goals, we examine a random parameter model, empirical distributions of Cronbach's α, and a simulation study. Data containing brain activity values of 37 participants in a Eriksen Flanker experiment is used. It turns out that ERPs are independent of error trials and that taking a specific set of errors to compute α can significantly bias the number of errors needed for internal consistency.