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"> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal;"><span style="font-size: 10pt; font-family: &quot;Courier New&quot;;">Date:<span style="">&nbsp;&nbsp;&nbsp; </span>Thu, 12 Mar 2009 11:04:18 -0700<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal;"><span style="font-size: 10pt; font-family: &quot;Courier New&quot;;">From:<span style="">&nbsp;&nbsp;&nbsp; </span>"Landsberger, David" <a href="mailto:DLandsberger@xxxxxxxx"><span style="color: blue;">&lt;DLandsberger@xxxxxxxx&gt;</span></a><o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal;"><span style="font-size: 10pt; font-family: &quot;Courier New&quot;;">Subject: Interpreting a negative d'<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal;"><span style="font-size: 10pt; font-family: &quot;Courier New&quot;;"><o:p>&nbsp;</o:p></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal;"><span style="font-size: 10pt; font-family: &quot;Courier New&quot;;">I have conducted an experiment where I have obtained for one subject in one<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal;"><span style="font-size: 10pt; font-family: &quot;Courier New&quot;;">condition a negative d' which I cannot explain. I was hoping that someone<o:p></o:p></span></p> <p class="MsoNormal" style="margin-bottom: 0.0001pt; line-height: normal;"><span style="font-size: 10pt; font-family: &quot;Courier New&quot;;">here might be able to offer me some insight.<o:p></o:p></span></p> <p class="MsoNormal"><o:p>&nbsp;</o:p></p> <p class="MsoNormal">Hello, David,</p> <p class="MsoNormal">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) &#8211; what the correct response probability would be if the O were playing the game properly.</p> <p class="MsoNormal">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.<span style="">&nbsp; </span>Then the obtained correct percentage in the experiment, P(obt) would be : P(obt)=[1-P(c)]*0.5 and then the &#8220;real&#8221; P(c) could in fact be calculated:</p> <p class="MsoNormal">P(c) = 1-[P(obt)/0.5]</p> <p class="MsoNormal">And with this the case, obtained P(obt) could range from 0-50%, and <span style="">&nbsp;</span>when underlying P(c) is greater than 33% &#8211; and thus when obtained P(obt) - is less than 33% you would see negative d&#8217; values.</p> <p class="MsoNormal">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 &#8220;real&#8221; d&#8217; found in the tables.</p> <p class="MsoNormal">I hope all this has not simply confused the issue even further.</p> <p class="MsoNormal">All good wishes,</p> <p class="MsoNormal">Doug Creelman</p> <pre class="moz-signature" cols="72">-- C. Douglas Creelman 416-690-9407 (phone &amp; 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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