Figure 9 depicts the sensitivity (top row) and mean RT collapsed over display types (bottom row). There was a clear effect of 3D relatability on both measures. Sensitivity was larger and RT was smaller in the 3D relatable relative to nonrelatable displays. Both d-prime and RT results show a strong improvement of performance with increasing slant of the inducing surfaces. No meaningful differences appeared between aligned vs. misaligned displays for either sensitivity or RT. Finally, the performance advantage due to 3D relatability decreased with increasing slant.
These observations were confirmed by the statistical analyses on d-prime and RT values. We analyzed d-primes in a 5 (inducing surface slant) × 2 (3D relatability) × 2 (apertures alignment) repeated measures ANOVA and RTs in a similar design with the addition of display type (parallel, converging) as a factor. The main effect of 3D relatability was significant for both d-prime (F1, 25 = 20.96, p < 0.001) and RT (F1, 25 = 20.52, p < 0.001). The amount of increase in sensitivity due to 3D relatability was on the order of 0.31 (mean d-prime = 2.58 vs. 2.27 for 3D relatable vs. nonrelatable displays), which equated to 9% of our corrected d-prime scale. Similarly, the amount of reduction in the time needed to perform the classification task due to 3D relatability was of about 91 ms (mean RT = 1.22 vs. 1.31 s for 3D relatable vs. nonrelatable displays), equating to 7.2% of the global average RT of 1.26 s. The main effect of simulated slant of the inducing surfaces was also significant, with d-prime increasing (F4, 100 = 184.5, p < 0.001) and RT decreasing (F4, 100 = 54.19, p < 0.0001) as a function of simulated slant. There was no main effect for the alignment of aperture pairs for either d-prime or RT, consistent with the idea that the spread of surface qualities does not depend on particular aperture positions or their alignment relative to the direction of tilt of the inducing surfaces.
The surfaces slant × 3D relatability interaction was significant for both d-prime (F4, 92 = 10.4, p < 0.0001) and RTs (F4, 92 = 5.22, p < 0.001). A post-hoc analysis suggested that this effect was due to the decreasing differences between 3D relatable and nonrelatable displays at increasing slant values in a direction consistent with the effectiveness of the 90-deg constraint. Indeed the performance gain due to 3D relatability (difference between individual d-primes and individual RT for 3D relatable vs. nonrelatable displays) was significantly different from 0 only for values of inducing surface slant smaller than the limiting slant values of 45 deg beyond which a violation of the 90-deg constraint occurs. The d-prime gains for θ = 20, 35, 46, 54, and 60 deg, respectively, were: 0.64 (t25 = 5.2, two tailed, p < 0.001), 0.54 (t25 = 5.02, two tailed, p < 0.001), 0.35 (t25 = 3.10, two tailed, p < 0.005), 0.13 (t25 = 1.15, two tailed, n.s.), and −0.11 (t25 = −1.38, two tailed, n.s.); while the RT gains were: −0.18 (t25 = −3.8, two tailed, p < 0.001), −0.15 (t25 = −4.5, two tailed, p < 0.001), −0.10 (t25 = −3.4, two tailed, p < 0.005), 0.03 (t25 = −1.71, two tailed, n.s.), and 0.00 (t25 = 0.2, two tailed, n.s.) s.
The effect of the display type on RT was not significant. However, the display type × inducing surface slant interaction was significant (F4,100 = 4.32, p < 0.01); RT decreased more steeply with increasing slant for converging displays than for parallel displays. This was confirmed by comparing changes in RT for displays with θ = 20 vs. 60 deg for converging relative to parallel displays (0.58 vs. 0.35 s: t25 = 2.5, two tailed, p < 0.05). Finally, consistent with the idea that 3D relatability should affect converging display more than parallel displays over inducing surface slant conditions, a significant display type × inducing surface slant × 3D relatability interaction was found (F4, 100 = 3.1, p < 0.05).