Experimental or behavioral variables that vary from trial to trial are often ignored or amalgamated, thereby reducing “many” to “few.” The logic behind trial averaging is that, at the single-trial level, brain measurement tools (EEG, MEG, fMRI) and the neurocognitive systems they measure contain more noise than signal; thus, by averaging data over many trials of the same or similar experiment condition, signal-to-noise ratio increases and randomly distributed variance averages out. This reasoning is irrefutable – the influence of noise decreases as a function of the number of trials and some cross-trial variance is unrelated to the hypotheses under investigation. In other situations, however, hypotheses must or should be tested using data from single trials within subjects, for example when linking neural dynamics to response time (Weissman et al., 2006; Yarkoni et al., 2009), visual stimulus parameters (Rousselet et al., 2008; Scholte et al., 2009), decision-making (Philiastides and Sajda, 2007; Ratcliff et al., 2009), or other parameters that vary from trial to trial.
