# Re: Back to the piano ... ("Timothy C. Justus" )

```Subject: Re: Back to the piano ...
From:    "Timothy C. Justus"  <Timothy.C.Justus(at)DARTMOUTH.EDU>
Date:    Fri, 23 Oct 1998 05:12:11 EDT

The essential parts of Jim Beauchamp's message are quoted at the =
end of my message...

To answer the question about my posting, yes, different points on =
the same curve in an ROC could represent different subjects with =
different biases, or perhaps the same subject under different =
experimental manipulations of bias.  For example of the latter (a =
rather rough one), providing a reward for a correct identification =
of a  piano tone (hit), while being indifferent to an incorrect =
identification of a synthetic tone (false alarm), would bias the =
subject to answer "piano tone" more often, increasing both H and F.=20

I agree that the choice of D =3D 50% as the "indistinguishability =
threshold" is not logical; this number does not indicate chance =
performance if we are using D =3D H - F.  With this measure, scores =
near *zero* would indicate low discrimination, while scores =
significantly above zero (or below for that matter) would indicate =
higher discrimination.  Something as simple as a t-test comparing =
the population of D values to 0 could tell you if these synthesized =
tones are passing for the real thing.

In the case of P =3D .5 + .5D, Jim is right that a P of .50 would =
indicate guessing, since as we have said, D would be 0 in this =
case.  100% would indicate perfect discrimination and =
categorization.  Incidentally, 0 would also indicate perfect =
discrimination.  The subject can tell the difference but merely has =
the labels backwards.

Timothy Justus
Dartmouth College

--- "James W. Beauchamp" wrote:
What threw me off was my friend's assertion that D =3D 50% could be =
taken as
the "indistinguishability threshold", and since the results were =
below that
threshold, the synthetic tones were therefore considered to be
"indistinguishable" from the originals. However, it seems to me =
that D =3D 50%
is rather arbitrary, and my friend's scores do in fact indicate =
that some
degree of discrimination is going on. Would you agree?

Anyway, doesn't presenting the D scores (as I defined it above) =
accomplish
the same thing? If a point is above the diagonal, then D =3D H - F =
> 0.
The advantage of the D scores is that they are probably easy to =
understand
by the typical reader of a sound synthesis article.

Another way to present the data would be percent correct, P. In =
this case,
P =3D .5*(H + (1-F)) =3D .5 + .5*D
So we see that this is just a rescaling of the D data where, in =
this case,
100% corresponds to perfect discrimination (or catagorization) and =
50% is
the guessing threshold.

--- end of quote ---

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```

This message came from the mail archive
http://www.auditory.org/postings/1998/
maintained by:
DAn Ellis <dpwe@ee.columbia.edu>
Electrical Engineering Dept., Columbia University