Figure 10.

Linked perceptual gain and noise constrains the locus of bias weighting. A plots perceptual noise as a function of perceptual gain for both leftward (open symbols) and rightward (filled symbols) choices, all three biased conditions, and all eight cases (48 points). Each symbol shape represents data from one case. Across subjects, this correlation was significant (Pearson's R, r = 0.68, p < 0.0001); within subjects, the correlation was significant in five individual cases (p < 0.05). Perceptual noise has the units of the stimulus (d′); perceptual gain is unitless. B is a schematic of a mechanism that can account for all of our observations. An input sensory signal is perturbed by visual internal noise (σ_v). Both are then scaled by an extraretinal weighting factor (w) before the split between perceptual and motor-output pathways, thus accounting for the correlation between the gain and noise of the percept and between both of these and saccade bias. Additional sources of output noise (σ_p and σ_m) are then added to the scaled signal, introducing unshared variability into the percept and saccadic choices, predicting an overall perceptual noise of ${\sigma }_{\text{perceptual}}=\sqrt{{\left({\sigma }_{v}w\right)}^2+{\sigma }_p^2}$ (solid black line in A). Last, a normalization process prevents the attentional weight from causing a change in perceived overall brightness.