Repeated-measures analyses with the subject treated as a random effect in a mixed-effects model (linear mixed-effects model using package nlme in R,
http://www.r-project.org/) were run on the motion-in-depth estimation data. Independent variables were stimulus (texture vs. dot), reference (fixed stimulus pattern for relative disparity and looming signals present or not: alone vs. relative), and condition. Condition referred to the vergence-looming combination (looming only, normal, vergence only, vergence reversed, or vergence increased). For some analyses the condition was instead decomposed into separate independent variables for specified vergence (nominally 0, 20, 20, −20, and 40 cm for the five conditions, respectively) and the specified looming (20, 20, 0, 20, and 20 cm for the five conditions, respectively). As the conditions did not represent balanced or factorial combinations of looming and disparity, analysis was performed on subsets of conditions to investigate the experimental hypotheses. One outlier data point was identified in the reversed-vergence dot-relative condition and removed. In this case, the subject reported large motion in depth in the direction of the looming cue (compared to the typical percept in the direction of target vergence) that was more than two standard deviations from the mean of the rest of the data.
Analysis of the full dataset (except the effects of attention on the reference stimulus in the vergence-reversed condition, see below) demonstrated a significant interaction between stimulus and condition, F(4, 95) = 19.58, p < 0.001, as well as main effects of reference, stimulus, and condition, F(1, 95) = 15.53, p < 0.001; F(1, 95) = 27.64, p < 0.001; and F(4, 95) = 28.10, p < 0.001, respectively. There was also a marginal interaction between reference and condition, F(4, 95) = 2.25, p < 0.07. We will address this possible interaction below when looking at the effects of disparity and looming on perceived motion in depth. In the conditions with reference, there was no ambiguity about the motion and subjects reported that the moving dichoptic stimulus appeared to move while the fixed surface was stationary.
Due to the qualitative differences in various conditions it is difficult to interpret these interactions and it is more informative to look at planned contrasts in subsets of the data.