Variance (un)explained: Experimental conditions and temporal dependencies explain similarly small proportions of reaction time variability in linear models of perceptual and cognitive tasks

Any series of sensorimotor actions shows fluctuations in speed and accuracy from repetition to repetition, even when the sensory input and motor output requirements remain identical over time. Such fluctuations are particularly prominent in reaction time (RT) series from laboratory neurocognitive tasks. Despite their omnipresent nature, trial-to-trial fluctuations remain poorly understood. Here, we systematically analysed RT series from various neurocognitive tasks, quantifying how much of the total trial-to-trial RT variance can be explained with general linear models (GLMs) by three sources of variability that are frequently investigated in behavioural and neuroscientific research: 1) experimental conditions, employed to induce systematic patterns in variability, 2) short-term temporal dependencies as the autocorrelation between subsequent trials, and 3) long-term temporal trends over experimental blocks and sessions. Furthermore, we examined to what extent the explained variances by these sources are shared or unique. We analysed 1913 unique RT series from 30 different cognitive control and perception-based tasks. On average, the three sources together explained ∼8-17% of the total variance. The experimental conditions explained on average ∼2.5-3.5% but did not share explained variance with temporal dependencies. Thus, the largest part of the trial-to-trial fluctuations in RT remained unexplained by these three sources. Unexplained fluctuations may take on non-linear forms that are not picked up by GLMs. They may also be partially attributable to observable endogenous factors such as fluctuations in brain activity and bodily states. Still, some extent of randomness may be a feature of the neurobiological system rather than just nuisance. Public significance statement When we perform stereotyped repetitive sensorimotor actions, these nevertheless exhibit remarkable variability over time even under laboratory conditions. We show that most of this variability is not explained by linear models including two factors frequently studied in experimental psychology or cognitive neuroscience: the manipulations introduced by the experimenters and endogenous temporal dependencies that arise over multiple timescales. This implies that moment-to-moment fluctuations in typical behavioural data are largely unpredictable by linear models. Endogenous processes may also influence these fluctuations even in highly stable environments. It remains an empirical question to what extent exogenous and endogenous sources influence fluctuations non-linearly. ### Competing Interest Statement The authors have declared no competing interest.