Supplementary Figure 4: Statistics of Experiment 1 trial sequences.

Experiment 1 used two approaches for generating trial sequences: a fully random sequence of orientations and a counterbalanced sequence designed to ensure that every orientation used in the analysis was preceded equally often by all orientations in the range of -60 to 60 degrees relative to it (see Methods). Data points here show the autocorrelation (correlation between the orientation presented on a given trial and the relative orientation of the previous trial) for each run that subjects completed in Experiment 1; one point represents one run. Within the counterbalanced design, the autocorrelation was exactly zero for all runs when considering the trials used in the analysis (“baseline” trials; red data). Considering all trials within the counterbalanced runs including those not intended for analysis and discarded prior to computing the strength of serial dependence, the correlation tended to be positive (blue data) and the mean was significantly greater than zero (mean correlation of z = 0.11 across 40 runs; P = 1x10^-5, evaluated by a permutation test in which we shuffled the trial ordering within runs and recomputed the mean correlation 100,000 times to generate a null distribution). However, there was no significant difference in the amplitude of serial dependence measured within only baseline trials vs. all trials in the counterbalanced sequences (group mean amplitudes were ±5.51° for all trials (1030 trials per subject) and ±8.19° for baseline trials (260 trials per subject); P = 0.10; permutation test). Within the randomized stimulus sequences, the autocorrelation was never exactly zero (which is why we also employed a counterbalanced design), but across all runs the autocorrelation centered on zero and did not significantly differ from zero (green data; mean correlation of z = -0.025 across 32 runs; P = .15 evaluated with a permutation test as above). Within both the counterbalanced and randomized paradigms, we found significant serial dependence in orientation perception for all subjects. These results, together with the negative aftereffect modeling (Supplementary Fig. 5), confirm that perceptual serial dependence is not the result of statistical dependencies in the presented trial sequences.