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[AUDITORY] question about c SOLVED!

Dear list,

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.

Thanks again!

Dr. Samuel R. Mathias
Center for Computational Neuroscience and Neural Technology
Boston University
677 Beacon St., Boston, MA 02215