Subject: [AUDITORY] question about c SOLVED! From: Sam Mathias <smathias@xxxxxxxx> Date: Wed, 18 Sep 2013 14:54:12 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>--001a11c2e2248ee94c04e6acf66b Content-Type: text/plain; charset=ISO-8859-1 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 --001a11c2e2248ee94c04e6acf66b Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: quoted-printable <div dir=3D"ltr">Dear list,<div><br></div><div>Many thanks to everyone that= replied regarding my question. Based on these comments and some simulation= s I ran, I think I have the solution, which I thought I'd share with ev= eryone.</div> <div><br></div><div>In a nutshell, it turns out that c =3D -0.5 * [z(H) + z= (F)] is a perfectly fine measure of response bias for 2I2AFC. However, it d= oes not yield what I call the "true criterion", which I explain b= elow.</div> <div><br></div><div>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 bet= ween them, y =3D 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".</d= iv> <div><br></div><div>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 pyth= on code to illustrate this on request.</div><div><br></div><div>Thanks agai= n!</div> <div><br></div><div><div>--=A0<br>Dr. Samuel R. Mathias<br>Center for Compu= tational Neuroscience and Neural Technology<br>Boston University<div>677 Be= acon St.,=A0Boston, MA 02215<br><div><br></div><div><br></div></div></div> <div dir=3D"ltr"><br></div></div></div> --001a11c2e2248ee94c04e6acf66b--