Supplementary Figure 3: Serial dependence measured using randomized trial sequences.

We repeated Experiment 1, this time presenting a random sequence of orientations on each run. All aspects of the experimental design and analysis were identical to the counterbalanced version of Experiment 1 except that a random orientation was presented on each trial, and we analyzed all trials in the sequence. Four participants each completed eight 104-trial runs. The gray line in each plot shows a running average of the subject's orientation judgment errors, and data points show mean error within 20 deg. bins along the abscissa. Black lines show derivative of Gaussian (DoG) fits to subjects' error distributions. Each subject individually showed significant serial dependence in orientation judgments (permutation tests; 824 data points per subject). The amplitude of serial dependence found with this randomized design did not differ from the amplitude measured with the counterbalanced design (group mean amplitudes were ±8.19° for the counterbalanced design (4 subjects, 260 data points per subject) and ±4.85° for the randomized design (4 subjects, 824 data points per subject); permutation test comparing amplitudes from the randomized and counterbalanced versions; P = 0.15).