GRAPHIC PRESENTATION OF DATA FROM 2D-SC EXPERIMENTS
The two sequences of figures show the manner in which trials are accumulated in the two-dimensional stimulus-classification task used by Dye et al. The target interaural difference of time (IDT) is randomly selected from one of ten different values on each trial, five IDTs leading to right channel and five leading to the left. The IDT of the distractor also takes on one of ten different values on each trial (usually the same ten values as the target). Each of the possible different combinations of target and distractor IDT is presented in a block of 100 trials, with the order of presentation randomized. Listeners are instructed to indicate whether the target appears to the left or right of the intracranial midline. A diotic presentation of the target alone precedes each target + distractor interval, and feedback is given after each trial.
The first sequence depicts the accumulation of responses for a condition in which judgments of target laterality are independent of the distractor delay.
Plotted is the number of "Left" responses as a joint function of the target and distractor delays as the number of replications goes from 1 to 3 to 5 to 10
to 15 and finally to 20 (the absence of "Left" responses for a given cell indicates that "Right" responses were elicited). Note that for this particular
condition the left and right responses are partitioned by a boundary running along x=0.0.
The second sequence shows the accumulation of responses for a condition in which responses are based on an average of the information derived from the targetand the distractor with the two components weighted equally. Note that left and right responses are partitioned by a boundary that runs along y=-x.
At times it is desirable to present data in the form of color-coded contour maps. Examples of these are provided for the two conditions from above.
A variation on the 2D-SC task is to independently select the interaural delays of the target and the distractor from Gaussian distributions with means of 0.0 and a standard deviation of, say, 100 micorsec. Again, the listeners' task is to indicate whether the target appears to the left or right of the intracranial midline. Examples of the responses elicited for 1500 such trials are shown in the two figures below, one for a condition in which the target responses are independent of the distractor IDT and one for a condition in which the target and distractor are weighted equally.
Assume that the Decision Variable is a weighted combination of the information arising from the target and distractor components,
where 
i is the weight given to the ith component, IDTi is its interaural difference of time, and 
is Gaussian noise (mean of 0). IDTs favoring the left
ear are assigned a negative valence and those favoring the right ear are assigned a positive valence. If C is the criterion for making a "RIGHT"
response, then
If DV>C, respond "RIGHT."
If DV<C, respond "LEFT."
A listener who performs the task analytically (like the first sequence of response matrices) gives no weight to the distractors so that the decision variable
is the target interaural delay. A listener who performs the task synthetically (like the second sequence of matrices) gives equal weight to the target and
distractor interaural delay.
The component weights are computed in one of two ways: (1). The best-fitting linear boundary between left and right responses is found that minimizes
the RMS error. That slope is equivalent to -(Target/Distractor). (2). When more than one distractor is used, the weights are derived from the
point-biserial correlations between the responses (left/right) made by a listener and the IDTs associated with each of the components: r(Resp., IDT1),
r(Resp.,IDT2), r(Resp.,IDT3),....r(Resp.,IDTN).