Variable, sometimes absent, but never negative: Applying multilevel models of variability to the backward crosstalk effect to find theoretical constraints.

When performing two tasks at the same time, the congruency of the second task's features influences performance in the first task. This is called the backward crosstalk effect (BCE), a phenomenon that influences both theories of binding and of dual-task capacity limitations. The question of whether the BCE is found in all participants at all times is relevant for understanding the basis of the effect. For example, if the BCE is based on strategic choices, it can be variable, but if it is automatic and involuntary, it should never vary in whether it is present or not. Variability in observed BCE sizes was already documented and discussed when the group average effect was first reported (Hommel, 1998). Yet the theories discussed at the time did not motivate a more direct analysis of this variability, nor did the readily available statistical tools permit it. Some statistical approaches recently applied in cognitive psychology allow such a variability-focused analysis and some more recent theoretical debates would benefit from this as well. We assessed the variability of the BCE as well as a BCE-like free-choice congruency effect by applying a Bayesian multilevel modeling approach to the data from a dual-tasking experiment. Trials consisted of a two- and a four-response task. We manipulated which task was presented first and whether the response to the four-choice task was free or forced choice. RT data were best predicted by a model in which the BCE is zero in part of the population and drawn from a normal distribution truncated at zero (and thus always positive) in the rest of the population. Choice congruency bias data were best predicted by a model assuming this effect to be drawn from a normal distribution truncated at zero (but, in contrast to the RT data, without the subset of the population where it is zero). The BCE is not an inflexible and universal phenomenon that is directly linked to an inherent structural trait of human cognition. We discuss theoretical constraints implied by these results with a focus on what we can infer about the traits of the factors that influence BCE size. We suggest that future research might add further major constraints by using multi-session experiments to distinguish between-person and within-person variability. Our results show that the BCE is variable. The next step is understanding along which axes it is variable and why it varies.