I would very much like to see a reply from Neil Macmillan or Doug Creelman to your proposed model. However, beyond the question I have on the observer's evaluation of H and F (which, themselves, could also have biases even if the person has a perfect memory for the history of his/her past responses), I would surmise that the recency effect would give the x2 trace a larger weight and, therefore, put a second-interval bias on y and, consequently, also on k.
On 9/18/13 11:54 AM, "Sam Mathias" <smathias@xxxxxx> wrote:
Many thanks to everyone that replied regarding my question. Based on these comments and some simulations I ran, I think I have the solution, which I thought I'd share with everyone.
In a nutshell, it turns out that c = -0.5 * [z(H) + z(F)] is a perfectly fine measure of response bias for 2I2AFC. However, it does not yield what I call the "true criterion", which I explain below.
Imagine that on each trial, the listener generates two observations, x1 and x2, which are Gaussian random variables with different means but the same variance. The listener then computes the difference between them, y = x2 - x1, and compares this value to a criterion. To avoid confusion, I call this the "true criterion", k. If y > k, the listener responds "2nd", otherwise responding "1st".
To get k, one needs to calculate c using the eq. above, and then MULTIPLY the result by sqrt(2). I'm happy to supply some python code to illustrate this on request.
Dr. Samuel R. Mathias
Center for Computational Neuroscience and Neural Technology
677 Beacon St., Boston, MA 02215