To check if optic flow similarity index predicts detection rates, we applied GLME models using the R “lme4” package (version 1.1–28;
Bates et al., 2015) in the R programming environment (version 4.1.1, R Core team, 2019). The binary variable Detect was the dependent variable, and optic flow similarity index, and change direction were the predictor variables. Similar to the previous experiments, a model comparison analysis between the maximal and the minimal models (i.e. with and without the random slopes) did not reveal a statistically significant difference (χ
2 = 69.046,
P = 0.509). Accordingly, participants and trials were accounted for as random effects at the intercept level thus discounting the effects of random slopes. See the
Appendix (
Table A3 and
Figure A3) for model estimates and estimate plot. Drop1 predictor model comparisons revealed significant main effect of direction (χ
2 = 82.01,
P < 0.001), and a significant main effect of magnitude (χ
2 = 25.452,
P < 0.001). On average, detection accuracy was lower for skip-ahead jumps compared to the re-view jumps (re-view: M = 0.87, SEM = 0.13 and skip-ahead: M = 0.75, SEM = 0.12). Detection accuracy also increased as a function of jump magnitude (500 ms: M = 0.81, SEM = 0.14; 1000 ms: M = 0.87, SEM = 0.13; and 2000 ms: M = 0.90, SEM = 0.15) – replicating the findings from
Experiments 1 and
2. There was no significant main effect of optic flow similarity (χ
2 = 0). However, the interaction between direction and optic flow similarity was significant (χ
2 = 19.9,
P < 0.001). On average, detection accuracy for skip-ahead condition decreased with increased optic flow similarity (500 ms: slope = −0.636, SE = 0.272; 1000 ms: slope = −0.489, SE = 0.305; and 2000 msec: slope = −0.796, SE = 0.568). We observed the opposite trend for the re-view condition – where detection accuracy increased with increased optic flow similarity (500 ms: slope = 1.067, SE = 0.286; 1000 ms: slope = 1.215, SE = 0.333; and 2000 ms: slope = 0.908, SE = 0.599) - see
Figure 9. The interaction between magnitude and optic flow similarity was not significant (χ
2 = 0.4,
P = 0.818). We therefore conducted post hoc analyses ignoring the magnitude variable – thus collapsing the data into skip-ahead and re-view conditions. Tukey's post hoc analysis comparing the skip-ahead and re-view conditions showed a significant difference in the trends between the two conditions (re-view – skip-ahead: estimate = 1.7, SE = 0.379, z = 4.491,
P < 0.001). These results show that optic flow similarity affects detection rate differently for re-view versus skip-ahead conditions.