As discussed above, the whole-report task allowed us to analyze the joint distribution of stimulus reports within a trial. Several models of delayed estimation assume that stimuli are encoded independently—if this is the case, then the joint distribution of within-trial reports should be uniform.
Figure 2B shows example within-trial joint distributions for set size six of the participant-ordered continuous whole-report task. Each panel corresponds to the joint distribution between the first and the
nth color reported within the same trial. Note that the joint distribution of two circular variables lies on the surface of a torus. This means that a point in the upper-left or bottom-right of panels in
Figure 2B represents two values very near each other in circular space. Two dependencies are apparent: Participants tended to report similar colors for the first and second reports in a trial, and they tended to avoid reporting colors similar to the first with later reports. This is not unique to the first report, as consecutive reports are similar regardless of when in the trial they occurred.
Another way to visualize this is to compute the relative angular distance between two colors reported in the same trial (
Figure 2A). The upper panel of
Figure 2C shows relative distance distributions computed for the continuous whole-report task at set size six. The pattern of dependencies described above is evident for the participant-ordered condition.
Deviations from uniformity are also evident for the randomly ordered report condition, even though the corresponding distributions of
presented values were uniform. Critically, this effect was not driven by a few participants making idiosyncratic reports but was consistent across all participants (
Supplementary Figure S3) and set sizes (
Supplementary Figure S4).
Deviations from uniformity are evident for the discrete whole-report task, and patterns of dependence were qualitatively similar to those evident in the continuous task data, with one key difference—in both conditions of the discrete task, participants rarely repeated their first report later in the trial. This suggests that participants were not simply reporting the same color repeatedly but explicitly avoiding previous colors while consecutively reporting similar colors.
We quantified dependence between within-trial reports using KL divergence, a measure of the statistical distance between two distributions. For each participant, report condition, and pair of reports, we estimated the KL divergence between the relative distance distribution and a circular uniform distribution. We compared these KL divergence estimates to a baseline divergence obtained by repeating this process using a size-matched circular uniform sample. This process was bootstrapped to obtain an estimate of uncertainty (see Methods for details), and median KL divergence estimates for each participant are shown alongside corresponding baseline estimates in the lower panels of
Figures 2C and
2D. This analysis confirmed that distributions of within-trial relative distance often deviated from uniformity for all participants of both tasks. Divergences tended to be higher in the participant-ordered condition than in the randomly ordered condition and were highest for consecutive reports.
Repeated-measures ANOVAs using estimate type (i.e., data vs. baseline) and report pair as within-subject factors confirmed a significant effect of estimate type on KL divergence in both the participant-ordered, F(1, 21) = 70.49, p = 3.76 × 10–8, and randomly ordered, F(1, 16) = 10.55, p = 0.005, conditions of the continuous task. The same analysis confirmed a significant effect in both the participant-ordered, F(1, 13) = 55.13, p = 5.0 × 10–6, and randomly ordered, F(1, 13) = 32.74, p = 7.0 × 10–5, conditions of the discrete task. These analyses also showed significant effects of report order, as well as an interaction between report order and estimate type.