Investigating the effect of response autocorrelation on <i>n</i> -back analyses of serial dependence

Perception and decision-making in the present are not solely driven by the current inputs reaching sensory organs, but are also influenced by previous stimuli and decisions (i.e., task responses). This "serial dependence" effect is not limited to the immediately preceding stimulus or response, but it has been shown to extend several trials back in the past. However, owing to potential correlations across past responses, effects from more remote trials may be inflated, even when assessing the effect of past stimuli. In this work, we assess the potential role of response autocorrelation as a potential source of spurious results. We first show that, in serial dependence models, the effect of responses decays slowly across trials, and that such a slow decay increases the probability of observing spurious effects, even when considering past stimuli. We then provide an analytical tool to contain such spurious results. Finally, we apply our approach to a real dataset from a previous study, showing that the effect from two trials back may indeed be inflated. Our results suggest that serial dependence may be more limited in time than previously thought, and that caution is in order when assessing effects from multiple trials back in the past.