# [AUDITORY] question about c SOLVED! (Sam Mathias )

```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>

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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

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<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&#39;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 &quot;true criterion&quot;, 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 &quot;true criterion&quot;, k. If y &gt; k, the =
listener responds &quot;2nd&quot;, otherwise responding &quot;1st&quot;.</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&#39;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>

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