Negative d' - 3AFC (Douglas Creelman )

Subject: Negative d' - 3AFC From: Douglas Creelman <creelman@xxxxxxxx> Date: Fri, 13 Mar 2009 15:08:44 -0400 List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY> This is a multi-part message in MIME format. --------------090700020007030907080002 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit Date: Thu, 12 Mar 2009 11:04:18 -0700 From: "Landsberger, David" <DLandsberger@xxxxxxxx> <mailto:DLandsberger@xxxxxxxx> 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) 9 Fernwood Park Ave. 416-708-9407 (cell) Toronto, ON Canada creelman@xxxxxxxx M4E 3E8 --------------090700020007030907080002 Content-Type: text/html; charset=ISO-8859-1 Content-Transfer-Encoding: 7bit <!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"> <html> <head> </head> <body bgcolor="#ffffff" text="#000000"> Date:    Thu, 12 Mar 2009 11:04:18 -0700<o:p></o:p> From:    "Landsberger, David" <a href="mailto:DLandsberger@xxxxxxxx"><DLandsberger@xxxxxxxx></a><o:p></o:p> Subject: Interpreting a negative d'<o:p></o:p> <o:p> </o:p> I have conducted an experiment where I have obtained for one subject in one<o:p></o:p> condition a negative d' which I cannot explain. I was hoping that someone<o:p></o:p> here might be able to offer me some insight.<o:p></o:p> <o:p> </o:p> 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 <pre class="moz-signature" cols="72">-- C. Douglas Creelman 416-690-9407 (phone & fax) 9 Fernwood Park Ave. 416-708-9407 (cell) Toronto, ON Canada <a class="moz-txt-link-abbreviated" href="mailto:creelman@xxxxxxxx">creelman@xxxxxxxx</a> M4E 3E8</pre> </body> </html> --------------090700020007030907080002--

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Electrical Engineering Dept., Columbia University