The stimulus-dependent nonlinearity could ameliorate the discrepancies between model and data. The stimulus-dependent nonlinearity, according to the literature, may reflect spatial uncertainty and nonlinear signal transduction (Abbey & Eckstein,
2006; Tjan & Nandy,
2006), which are related to the accounts of the lack of a feature map (Treisman & Souther,
1985), and of differential variability of search display (Palmer et al.,
2000; Rosenholtz,
1999; Rubenstein & Sagi,
1990), respectively. The accounts of the lack of a feature map can be considered as spatial uncertainty because logically speaking, a map for the absence of a feature denotes all locations without the feature, which usually covers most of the visual field. Spatial uncertainty in this situation is high, because only a tiny subset of “feature-absence map” corresponds to locations of objects without the feature. Nonlinear signal transduction will lead to differential variability among search items because the stimuli with higher intensity (e.g., signal plus noise image of the ROI in Q-stimulus) will have larger variance after accelerating nonlinear transduction than those with lower intensity (e.g., signal plus noise image of the ROI in O-stimulus). Thus, the evaluation of nonlinearity is important for understanding the determinant of search asymmetry. First, as
Figure 16C shows, a spatial uncertainty model (Manjeshwar & Wilson,
2001; Pelli,
1985) eliminated the “phantom” bar, a positive peak with the O stimulus, reflecting the effect of uncertainty of the bar location. Unlike human data, however, the model showed significant positive modulation for an O stimulus around the bar location compared with human data (
Figures 16C and
17). Grubbs' (
1950) test for outliers revealed that all three observers' data were significantly deviated from the uncertainty model in both O- and Q-search conditions (O-search:
G = 2.614,
G = 2.811,
G = 2.790; Q-search:
G = 2.729,
G = 2.894,
G = 2.653, for YU, TI, and JS, respectively; all
p < .01). More importantly, differences in modulation magnitude with the Q stimulus between O- and Q-search conditions, the signature of search asymmetry, were not significant (
Figure 18, two-tailed
t test,
t(9) = 0.095,
p = .92,
t(9) = 2.00,
p = .076, and
t(9) = 1.87,
p = .095 for YU, TI, and JS, respectively). Overall, spatial uncertainty could not account for the observed structure of human CI data, suggesting that hypotheses postulating spatial uncertainty as a critical factor are insufficient to account for the current data.