We fit a quadratic function using the least squares method to the U-shaped data of the observers (e.g., please see the curves in
Figs. 3a,
3b). We were able to fit the quadratic function to the data of all observers, except one (observer S7). This exceptional observer's data did not exhibit an increase in stereo threshold with increasing ICD owing to his low disparity thresholds being limited by our hardware's capability (monitor's spatial resolution). His data were thus excluded from this particular analysis. From each quadratic function, we derived the estimated ICD whereby the observer would have the lowest stereo threshold (i.e., the x-intercept at the minimum value of the quadratic function). We define this estimated ICD as the SED based on stereo threshold measurement (SED
stereo-threshold). By convention, we set a negative value of SED
stereo-threshold to indicate a dominant left eye.
Figures 3c and
3d plot the relationships of the observers' SED
stereo-threshold versus SED
inhibition and SED
stereo-threshold versus SED
combo, respectively. Because there is no significant difference in SED
stereo-threshold between the crossed and uncrossed disparity data (
t[7] = 0.100;
P = 0.923, two-tailed paired
t-test), we calculated their average and plotted these as a function of SED. Overall, the magnitudes of SED
stereo-threshold (0.061 ± 0.012 log unit) were much smaller than those of SED
inhibition (0.261 ± 0.058 log unit,
t(8) = 3.250,
P = 0.006, one-tailed paired
t-test) and SED
combo (0.318 ± 0.088 log unit,
t(8) = 2.760,
P = 0.012, one-tailed paired
t-test), with none exhibiting SED
stereo-threshold beyond ±0.2 log unit (the smallest ICD tested). All regression lines have reliable positive slopes (SED
stereo-threshold versus SED
inhibition:
r2 = 0.486,
P = 0.037 [or
rs2 = 0.614,
P = 0.013 with Spearman's rank correlation coefficient]; SED
stereo-threshold versus SED
combo:
r2 = 0.373,
P = 0.081 [or
rs2 = 0.444,
P = 0.0499 with Spearman's rank correlation coefficient]), indicating the same eye as dominant for the three different types of SEDs measured with the various binocular stimuli. Note that in the analysis above, we treated one observer's crossed disparity threshold as the average, as she (observer 10) was tested only in the crossed disparity condition. When we excluded this observer's data from the correlation analysis, a similar conclusion is reached (SED
stereo-threshold versus SED
inhibition:
r2 = 0.721,
P = 0.008 [or
rs2 = 0.580,
P = 0.028 with Spearman's rank correlation coefficient]; SED
stereo-threshold versus SED
combo:
r2 = 0.352,
P = 0.121 [or
rs2 = 0.383,
P = 0.102 with Spearman's rank correlation coefficient]).
We also estimated the minimal stereo threshold (stereo-thresholdmin) by using the minimum value of the quadratic function for each observer (i.e., the y-intercept at the minimum of the quadratic function). The average stereo-thresholdmin was 3.143 ± 0.405 arc min (mean of crossed and uncrossed disparity). These stereo-thresholdmin were smaller than when the two eyes received equal contrast half-images (3.447 ± 0.411arc min, t(8) = −2.322, P = 0.024, one-tailed paired t-test).