The majority of average errors in perceived speeds were negative, indicating that participants tended to underestimate the speed of the dot (
Figure 5), although there was a lot of variance across individuals (see error bars in
Figure 5), and it is also clear that the different speeds (slow, moderate, fast) seemed to be affected differently. A two-way repeated-measures ANOVA highlighted a significant interaction between presented speed and light scatter condition (
F(1.98, 25.72) = 4.66,
p = 0.019,
ε = 0.330,
ηp2 = 0.26). Because of this significant interaction, this means it was inappropriate to perform the standard tests of main effects, and so simple main effects were performed on the data.
Simple main effects do not identify a difference in performance across speeds for the baseline (no light scatter) condition (F(1.12, 14.60) = 3.50, p = 0.078, ε = 0.561, ηp2 = 0.21). However, significant differences of error were found for the mild level of scatter across the different presented speeds (F(1.02, 13.30) = 10.59, p = 0.006, ε = 0.512, ηp2 = 0.45). Bonferroni-corrected pairwise comparisons reveal this was driven by statistically significant differences between all presented speeds (2.5°/s vs. 5°/s, p = 0.012; 2.5°/s vs. 10°/s, p = 0.017; 5°/s vs. 10°/s, p = 0.026). The same effect of scatter was also reported for the moderate level of scatter (F(1.02, 13.24) = 16.73, p < 0.001, ε = 0.509, ηp2 = 0.56), driven by statistically significant differences between all presented speeds (2.5°/s vs. 5°/s, p = 0.007; 2.5 vs. 10, p = 0.004; 5°/s vs. 10°/s, p = 0.003). Similarly, the severe scatter condition also significantly affected performance differently across all speeds (F(1.40, 18.17) = 28.01, p < 0.001, ε = 0.699, ηp2 = 0.68), driven by statistically significant differences between all presented speeds (2.5°/s vs. 5°/s, p = 0.022; 2.5°/s vs. 10°/s, p < 0.001; 5°/s vs. 10°/s, p < 0.001). These comparisons indicate that the presence of light scatter affects speeds differently, which would have real-world implications given that the faster speeds are affected to the largest degree.
To investigate the effects of light scatter on each of the speeds, simple main effects were performed. These tests found no statistically significantly effect of light scatter condition on the slow speed (2.5°/s) stimulus (
F(1.90, 24.63) = 2.40,
p = 0.114,
ε = 0.634,
ηp2 = 0.16). However, increasing light scatter did significantly affect the perceived speed of the moderate speed (5°/s) stimulus (
F(3, 39) = 3.57,
p = 0.023,
ηp2 = 0.22). Similarly, increasing light scatter was also found to produce statistically significant differences within the fast speed (10°/s) stimulus (
F(1.42, 18.48) = 5.63,
p = 0.020,
ε = 0.474,
ηp2 = 0.30). For both the moderate and fast speed stimuli, significant main effects were driven by statistically significant differences between baseline performance relative to moderate levels of scatter and severe levels of scatter (see
Table 5;
Figure 5).
To provide some real-world context, the average difference in speed perception error between severe scatter and baseline conditions was calculated. For moderate speeds the difference in error was −0.50°/s, and for fast speeds it was −1.42°/s. This means that, on average, in the presence of severe scatter, a 5°/s stimulus was perceived as moving at 4.5°/s, and a 10°/s stimulus was perceived as moving at 8.58°/s. It is not straightforward to convert from degrees per second to miles per hour, but if the difference in speed is converted to a percentage, this difference can be understood as 10.0% reduction for moderate speeds and 14.2% reduction for fast speeds. This can be considered as equivalent to perceiving the speed of a 30 mph car as between 25.7 to 27.0 mph.