Fig 1.
Illustration of simulation procedure for a 4-AFC paradigm.
A) Model function used in this example (model threshold θ = 1.6 log10 arcsec). Each staircase (B) follows the rules described in the main text: starting at 3 log10 arcsec, decreasing the disparity by 0.15 log10 arcsec after a correct answer and increasing disparity by 0.45 log10 arcsec after an incorrect answer. Each row in (B) shows an example of one simulation with 80 trials. The left plots in (B) show the staircases: the ‘presented’ disparities for each simulation of the 80 trials. The right plots show the probability correct as a function of disparity, with the dots being the simulated data and the line the fitted psychometric function to the simulated data. From this fitted psychometric function the threshold value was estimated. After 10000 repeats, the estimated thresholds can be presented in an histogram (C) to show the distribution of likely thresholds that can result from the 4-AFC staircase procedure with this model psychometric function (A). The average of this ditribution can be compared with the model threshold as an indication of bias and precision of the 4-AFC staircase procedure.
Fig 2.
Age distributions of participants in both experiments.
The age distribution for the2-AFC task are presented on the left and for the 4-AFC on the right.
Fig 3.
Full screen examples of the stimuli in the 2-AFC and the 4-AFC task.
Panel (A) shows a practice trial of the 2-AFC task with line-interleaved elliptic dots. Right side shows the target stimulus: a squared patch standing out in depth from the background. Left side shows the distractor stimulus with only one depth plane. In addition to the disparity difference the target area is also presented in red. This colour/luminance cue is removed after the practice trials. (B) Example of the 4-AFC task with the target stimulus in the right upper quadrant. See dimensions in the main text.
Fig 4.
Simulation results for 2-AFC (top) and 4-AFC (bottom).
Each panel depicts the difference between the estimated thresholds and the model thresholds as a function of the model threshold (all in log10 arcsec). The average difference, plotted with open circles, is centred on zero, indicating no bias. Filled triangle symbols represent one standard deviation below and above the average difference. The asterisks show the median (around zero) and the 16th and 84th percentile. That the median and 16th and 84th percentiles respectively overlap with the mean and one SD below and above the mean indicate that the differences follow a normal distribution. The top row shows results for the 2-AFC task for a selection of number of trials (40, 60, and 80 trials). The bottom row shows results for the 4-AFC task for half the number of trials as the 2-AFC task (20, 30, and 40 trials).
Fig 5.
Results for 2-AFC (in red) and 4-AFC (in blue) with half the number of trials as the 2-AFC task are superimposed in the same graph. Each panel depicts the difference between the estimated threshold and the model threshold as a function of number of trials. The model threshold increases from the left to the right panel. The average difference, plotted with open circles, is centred on zero, indicating no bias. Filled triangle symbols represent one standard deviation below and above the average difference.
Fig 6.
Boxplot of stereothresholds (log10 arcsec) in 2-AFC and 4-AFC task (thresholds below 500 arcsec only).
Fig 7.
Average threshold estimates, uncertainty, precision and bias for the 2-AFC task (red full line) and the 4-AFC task (blue dotted line).
Error bars indicate 1 standard error above and below the average. Threshold uncertainty was calculated as the ratio between the simulated standard deviation and the threshold estimate. Bias and precision of threshold estimates were estimated by comparing the estimated thresholds after a subset of trials with the estimated threshold after the maximum number of trials (80). Bias is defined as the difference between both and precision as the absolute value of the bias.
Fig 8.
Experiment duration for different trial numbers, for the 2-AFC task (red solid line) and the 4-AFC task (blue dotted line).