Effect of passed time on switch probability and fixation duration within trials. (A) Effect of passed time on switch probability, using all trials. Switch probability for humans and aDDM peaked within 1 s of stimulus onset and gradually decreased thereafter. For the optimal model, the majority of attention switches were clustered around discrete time points. Note that the optimal model assumes the decision maker to use precise time estimates to drive attention switches. If we were to take into account the noisiness of human choice estimates (Buhusi and Meck, 2005), we would expect the optimal model curves to smoothen out and approach those of human data and the aDDM. (B–D) Effect of passed time on switch probability after dividing trials into upper and lower one-third of certain variables (B: RT, C: value sum, D: absolute value difference). When trials are split by RT (B), humans and aDDM featured a higher switch probability for longer (i.e. higher RT) trials. The optimal model featured comparable patterns within the time periods in which switches occurred. The dashed line indicates the point in time in which all trials were completed for the lower RT group. (E) Effect of passed time on fixation duration. Fixation duration increased with passed time for humans and the optimal model, suggesting that more time is allotted to each fixation as the trial becomes more difficult (human: ; optimal model: ). This trend is not seen in the aDDM which draws all middle fixations randomly from the same empirical distribution, therefore eliminating any effect of time on fixation duration within a single trial (). To compute the switch probability (A–D), we aligned all trials within each participant by stimulus onset, then counted the number of switches within each 0.2 s time bin. We then averaged the switch count in each time bin across trials to compute the switch probability. We only included time points up to when at least 1/3 of the total trials are included, and removed the last fixations since they are prematurely terminated when a decision is made. To split trials based on different variables, all trials within a participant were split into three equally sized bins based on the variable of interest. We plot the mean switch probability across participants, only including the first (green) and last (magenta) bins. At each time point, we performed a t-test across participants between the two bins, and marked all time points with a significant difference across bins with an asterisk (Bonferroni corrected; Bonferroni, 1936). For (E), whenever a new fixation occurred, we recorded its duration until the next fixation, excluding the first and last fixations. We averaged the fixation durations at each 0.05 s time bin across trials, dropping any time bin that contain data from less than 1/3 of all trials. We then plotted the mean fixation duration at each time bin across participants. Error bars indicate SEM across participants.