# Re: Back to the piano ...

```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.

I agree that the choice of D = 50% as the "indistinguishability threshold" is not logical; this number does not indicate chance performance if we are using D = 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 = .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 = 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 = 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 = 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 = .5*(H + (1-F)) = .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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