Fig. 2.

Calculating sensitivity to incidental correlations and simulating illusions: In this task (a) there are random fluctuations in the correspondence between action-outcomes on ‘no control’ trials that can be quantified by cross-correlation (b). Reverse correlation techniques found that participants were sensitive to these spurious correlations (c) and data simulated only from sensitivity to these correlations (red diamonds) recreated the ‘illusions of control’ seen on real trials (blue circles; both N = 48 d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)