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Negative d' - 3AFC

Date:    Thu, 12 Mar 2009 11:04:18 -0700

From:    "Landsberger, David" <DLandsberger@xxxxxxx>

Subject: Interpreting a negative d'


I have conducted an experiment where I have obtained for one subject in one

condition a negative d' which I cannot explain. I was hoping that someone

here might be able to offer me some insight.


Hello, David,

Here is my take on the situation: If the observer is seriously trying to be incorrect (ie. is so clueless not to respond randomly) then on those 3-Alternative forced-choice trials where the l(x) correctly yields the signal interval the Observer would randomly select one of the other intervals and be incorrect. Call the likelihood of this happening P(c) – what the correct response probability would be if the O were playing the game properly.

On those trials when the interval containing the largest l(x) is not the correct interval, 1-P(c), then the O would randomly select one of the remaining intervals and be correct half the time despite herself.  Then the obtained correct percentage in the experiment, P(obt) would be : P(obt)=[1-P(c)]*0.5 and then the “real” P(c) could in fact be calculated:

P(c) = 1-[P(obt)/0.5]

And with this the case, obtained P(obt) could range from 0-50%, and  when underlying P(c) is greater than 33% – and thus when obtained P(obt) - is less than 33% you would see negative d’ values.

All this presumes the departure from 33% is not within binomial variability, and that the observer is behaving consistently. If she is, then P(c) can be calculated and a “real” d’ found in the tables.

I hope all this has not simply confused the issue even further.

All good wishes,

Doug Creelman

C. Douglas Creelman             416-690-9407 (phone & fax)
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