# Re: Dprime and false alarm rates (Christophe Pallier )

```Subject: Re: Dprime and false alarm rates
From:    Christophe Pallier  <pallier(at)LSCP.EHESS.FR>
Date:    Tue, 18 Nov 2003 10:04:26 +0100

Erick Gallun wrote:

> Pawel,
>
> Would you be willing to explain briefly what those measures are?  I don't
> see how a reasonable statistic could account for a false alarm rate that
> reliably exceeds a hit rate unless the listener was using the wrong
> response label (i.e.- always calling the signal trials noise trials).  I
> suggested to Kala off-list that her listeners may be at chance, thus
> producing occasional results where the FAs exceed the hits.

I agree, but these things happen (just like negative d'), and trowing
away such participants is not the solution.

I once wrote a small note on A', which is available at
http://www.pallier.org/ressources/aprime/aprime.pdf
It shows how to compute A' and provide isocontours curves.
In a nutshell, A' is a estimate of the area under the ROC curve.
For points on the diagonal (FA=HIT), A'=0.5 and when FA>HITS, the point
in the (fa,hit) square is under the diagonal,
and the area is less than 0.5.

My reference for the computational formula was Snoodgrass and Corwin
(1988). J. Exp. Psychol., 117, p.38.

A nice feature of A', in  contrast to d', is that it is a number bewteen
0 and 1 and does not diverge when either
the FA or HIT rates reach 100% (these things also happen!).

Also, there is a paper by W. Donaldson (1993, Bull. Psychonomics
Society, 31(4), 271-274).
which suggests that A' maybe a more robust estimate of sensitivity than
d' (in the sense that it is more accurate
when the variance of the signal distribution differs from the variance
of the noise distribution)

Christophe Pallier (http://www.pallier.org)
Inserm u562, Orsay, France. (http://www.unicog.org)

Note: In the aprime.pdf paper cited above, I suggest that
dprime=z(hits)-z(fr) can be used in situations of discrimination,
but Kala Lakshminarayanan pointed out to me the MacMillan and Creelman
book and made me realise that there exists different models for the
discrimination task. Therefore, do not use dprime=z(hits)-z(fr) unless
you know what you are doing.
I will correct the note in aprime.pdf as soon as possible.

>
> At 03:55 PM 11/17/2003 +0100, Pawel Kusmierek wrote:
>
>> Kala Lakshminarayanan said:
>> > Has anyone had the
>> > problem of having false alarm rates that exceed the hit rate
>> sometimes and
>> > not being able to calculate dprime?
>>
>> You may want to check the nonparametric sensitivity and responsivity
>> measures, such as SI and RI (Frey and Collier 1973 Learn Motiv 4:327) or
>> A' and B'' (Grier 1971 Psychol Bull 75:424, see also Stanislaw and
>> Todorov
>> 1999 Behav Res Meth Instr Comput 31:13).
>>
```

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Electrical Engineering Dept., Columbia University