Does attentional selectivity in the flanker task improve discretely or gradually?

An important question is whether attentional selectivity improves discretely or continuously during stimulus processing. In a recent study, Hübner et al. (2010) found that the discrete Dual-Stage Two-Phase (DSTP) model accounted better for flanker-task data than various continuous-improvement models. However, in a subsequent study, White et al. (2011) introduced the continuous shrinking-spotlight (SSP) model and showed that it was superior to the DSTP model. From this result they concluded that attentional selectivity improves continuously rather than discretely. Because different stimuli and procedures were used in these two studies, though, we questioned that the superiority of the SSP model holds generally. Therefore, we fit the SSP model to Hübner et al.'s data and found that the DSTP model was again superior. A series of four experiments revealed that model superiority depends on the response-stimulus interval. Together, our results demonstrate that methodological details can be crucial for model selection, and that further comparisons between the models are needed before it can be decided whether attentional selectivity improves continuously or discretely.