Experimental schematics and procedure. (
A) CSF analysis. The CSF depicts how contrast sensitivity depends on SF. The inverse of the contrast threshold (
c–1) is contrast sensitivity (
S) at a particular SF. Bayesian inference was used to estimate the CSF parameters: peak-CS (maximum sensitivity), peak-SF (the most preferred SF), and bandwidth (closely related to CSF shape). Bandwidth was fixed across locations (see
Methods). Results of the cutoff-SF (highest discernable SF) and AULCSF (total sensitivity) are reported in
Supplementary Appendix. Higher values of these attributes are related to higher sensitivity, better performance, and/or a wider range of visible SFs and contrasts. (
B) Polar angle asymmetries. In many visual dimensions, performance is higher at the horizontal than the vertical meridian (HVA) and at the lower than the upper vertical meridian (VMA). (
C) Task. A test Gabor stimulus was presented briefly at one of the four polar angle locations, and participants judged its orientation (clockwise or counterclockwise). SF and contrast of the stimulus varied on each trial. (
D) Schematics of covariance analysis. The covariance of the three CSF attributes (peak-CS, peak-SF, bandwidth) for all three locations is a 9 × 9 matrix. The covariation of locations for each attribute (blue cells) and the covariation of attributes within each location (pink cells) were assessed. Covariance for bandwidth is shaded in gray because the bandwidth was identical across locations for each observer in the HBM and, thus, the covariance was not informative in most cases (but see
Figure 4). (
E) Interpretation of covariance analysis. Covariance of locations for each attribute (
D, blue cells) tests whether CSFs and their corresponding key attributes covary as a function of polar angle. For example, a perfect positive correlation (coefficient of 1) for peak-CS among locations X and Y indicates that an observer with a higher peak-CS at location X than other individuals also has a higher peak-CS at location Y (
E, blue panel, top). This relation does not hold for a scenario where there is no correlation (coefficient of 0) for any CSF attributes between locations X and Y. Covariance within each location (
D, pink cells) allows investigation of how individuals’ CSFs relate to one another within each location. A perfect positive covariation (correlation coefficient of 1) of all combinations of attributes within a location indicates that observers’ CSFs are organized diagonally in the SF-contrast space: The higher the peak-CS, the higher the peak-SF and the wider the bandwidth (
E, pink panel, top). The fewer the correlations, the greater the variability in the pattern of individual differences (
E, pink panel, bottom, is a scenario where no correlations are present among CSF attributes within a location).