Figure 10.

Analysis of linear separability for arbitrary target-distracter configurations in search space. (A) Schematic of the method used to assess linear separability for arbitrary configurations in search space; (T, D₁, D₂) depicts an arbitrary target-distracter configuration in which the target (T) is linearly nonseperable from its distracters (i.e., cannot be separated from the distracters using a single linear boundary). In this case, the target must fall along a straight line connecting the two distracters, implying that the sum of the two target-distracter distances will equal the distance between the distracters. The same target (T), however, is linearly separable from D₁ and D₃ (i.e., can be separated from the distracters using a linear boundary; right panel); in which case the sum of the target-distracter distances will exceed the distracter-distracter distance. The degree to which the sum exceeds the distracter-distracter distance can be taken as a measure of the degree to which the configuration is LS. (B) Taking the perceived distance between two objects to be the reciprocal of the corresponding search time, the distance between the distracters is plotted against the sum of the distances between the target and the two distracters. Search configurations that fall close to the unit line (y = x) in this plot were deemed LNS (plus symbols) whereas those that fall far from the unit line were deemed LS (triangles). Configurations that fall between these two groups are represented by circles. (C) Observed complex search distances against the model predictions—same y-axis data as in Figure 9B—but now with searches relabeled as LS (blue triangles) and LNS search configurations (red crosses) based on the method in (B). Model predictions were strongly correlated with the data in both groups, and the difference in correlation was not significant (LS, r = 0.72; LNS, r = 0.68; p = 0.76, Fisher's z test). Asterisks represent statistical significance (***** is p < 0.00005).