The direction noise and the size of serial dependence described above were calculated across the entire 360° circular angle space, assessing the overall precision and bias in pursuit direction. To examine whether there is any directional anisotropy in the precision of pursuit direction, we first divided the 360° circular angle space into eight segments based on the four cardinal directions (0° right, 90° up, 180° left, and 270° down) and the four oblique directions (45°, 135°, 225°, and 315°). Each segment was centered on one of these eight canonical directions, with angles varying by ±22.5°. The 90 trials of the ocular tracking task containing 90 target motion directions (2°–358° in 4° increments) were thus divided into eight data sets. To illustrate, trials with target directions of 2°, 6°, 10°, 14°, 18°, 22°, 338°, 342°, 346°, 350°, 354°, and 358° fell into the 0° canonical segment (i.e., 0° ± 22.5°). We pooled the data across participants, resulting in four cardinal (0°, 90°, 180°, and 270°) and four oblique (45°, 135°, 225°, and 315°) direction data sets for each participant group.
We measured the precision of pursuit direction around the four cardinal and the four oblique directions using the established method in previous studies.
35,36,47 Specifically, in each data set, we compared the pursuit direction in a given trial to the data set’s canonical direction and then converted it into a binary response (i.e., clockwise or counterclockwise relative to the canonical direction). We also computed the deviation of the target motion direction from the data set’s canonical direction in this trial, with positive values indicating counterclockwise deviations and negative values indicating clockwise deviations. For each data set, we plotted the percentage of counterclockwise binary pursuit responses across participants against the deviation of the target motion direction from the data set’s canonical direction. We then fitted the percentage data with a cumulative Gaussian function using the maximum likelihood method of the Palamedes Toolbox in MATLAB
48 to obtain an oculometric curve. The standard deviation (SD) of the best-fitting Gaussian, inversely related to the slope of the oculometric curve, served as an indicator of the precision of the pursuit direction. A smaller SD corresponds to a steeper oculometric curve, indicating a more precise pursuit direction response to the target motion direction.
We measured the directional anisotropy in serial dependence in pursuit direction by calculating the effect of previously seen target motion direction on current pursuit direction using the data from the four cardinal and the four oblique direction data sets. We calculated the size of serial dependence in each data set using the same method as described earlier in the “Serial Dependence Effect” section.