Fig. 1: Replications with orientation judgments with low-reliability targets.

a Navy symbols show the dispersion of reproductions of orientation (i.e. standard deviation) of broad oval stimuli (like those used in the original experiment—7 new participants), blue symbols thresholds from 2AFC judgments (9 participants). Thresholds (std or jnd) for targets flanked with ovals of the same orientation are plotted against those for unflanked targets. That most points lie below the equality line shows that the thresholds for the flanked targets were lower than for the unflanked. Reproduction precision was calculated as the standard deviation of the reproductions at four possible orientations (±35° and ±55°), with each participant completing at least 28 trials per condition. For 2AFC judgments precision was derived from the standard deviations of gaussian fits to psychometric functions like those of panel b (at least 110 trials per condition). b Psychometric curves for the aggregate participant (pooling data from all 9 participants), plotting the proportion of trials judged more clockwise than the 45° standard against the orientation of the target. Data are fitted by cumulative gaussian error functions. Black symbols and curve show data for the target alone; plum, violet, blue, celeste, and teal the flankers −60°, −30°, 0°, +30°, and +60° away from the target, gray orthogonal flankers. c Point of subjective equality (PSE) for the 2AFC judgments (aggregate participant) as a function of flanker–target orientation difference from −90° to +75° where negative values refer to flankers oriented counterclockwise of the target. PSE at 45° (dashed) indicated a veridical observer. Error bars are SEM calculated via bootstrap. d Two measures of error as a function of relative flanker orientation in the same dataset of (c): just noticeable differences (JND) in blue derived from psychometric functions, root mean square error (RMSE) in brown obtained by Pythagorean sum of biasing errors (PSE—45°) and scatter errors (JND), again for the aggregate participant. Horizontal dashed line indicates the JND in the unflanked condition and the yellow region indicates where performance is better than unflanked.