A 3-way ANOVA was run on the depth estimates with four levels of direction, three levels of blur and six values of offset (the 0 offset control was not included in this analysis because neither blur nor direction are defined when there is no shadow). The depth estimates for the 25 participants showed a strong (
F(5,120) = 280.2,
p < 0.001,
ηp2 = 0.92,
Pr = 1.0) increase with the offset of the shadow (
Figure 6). The effect of offset accounted for the major part of the data variance (
η2 = 0.57). Only three other effects reached significance — left versus right shadow offset, the interaction of offset with upper versus lower shadow position, and the interaction of offset with blur — and these explained far less of the variance (
η2 of 0.0002, 0.0035, and 0.0008, respectively). Specifically, there was a small but significant increase in depth (1.6%) for shadows on the right (equivalent to light from the left) versus on the left (
Figure 7A;
F(1,24) = 10.6,
p = 0.003,
ηp2 = 0.31,
Pr = 0.88). Second, there was a small but significant interaction between offset size and upper versus lower shadows (
F(5,120) = 5.1,
p < 0.001,
ηp2 = 0.18,
Pr = 0.98) with the lower shadows (equivalent to light from above) producing a slightly steeper slope (
Figure 7B). Finally, there was an interaction between blur and offset size (
F(10,240) = 4.6,
p < 0.001,
ηp2 = 0.16,
Pr = 0.99) with the no-blur results having a slightly lower slope than the two blurred cases (
Figure 7C). No other main effects or interactions were significant.
The control condition with no shadow was frequently judged as having no depth — 54% of all responses were zero. The rest of the settings indicated that some depth was seen by some observers on some trials. The average depth setting across all participants and trials was 0.07 ± 0.03 dva significantly greater than zero (t(23) = 2.34, p = 0.014) although the validity of the test is questionable as the distribution of settings is far from normal (the settings, perceived depth, cannot be negative).
We also analyzed the linear slope of depth versus offset. The slope fit to the average depth estimates across participants and conditions (including the 0 offset control condition) shown in
Figure 6 is 1.31 ± 0.04 and the intercept was 0.12 ± 0.04 dva. When the slope was fit with an intercept of zero, it was 1.40 ± 0.05, consistent with a direction of illumination (slant) of 35.5 degrees away from the surface normal. We then analyzed the slopes separately for each condition and participant based on the six offsets, excluding the no-shadow control. Here, the average of slopes fit individually for each participant and condition was 1.35 ± 0.07 (
Figure 7D) and ranged from 0.88 to 2.01. The difference in slopes for the four directions of shadow offsets is shown in
Figure 7D. The slope for the no blur conditions (not shown) was 7.9% lower than the average for the two blurred conditions.