Summarizing response bias in a detection experiment using the rating method

[Daniel Oberfeld <oberfeld@xxxxxxxxxxxx>]

Dear list,

sorry, this is not specifically an "auditory" question, but I 
nevertheless think that you are the right persons to ask...

I want to analyze data from a one-interval detection experiment where 
the subjects gave a response on a 4-category rating scale (1: "no tone" 
- 2: "probably no tone" - 3: "probably tone" - 4: "tone"). Thus, I can 
estimate 3 points on the ROC curve.

There are two experimental conditions in a within-subjects design and I 
want to test whether the listeners were more prone to respond that they 
heard a tone in one of the conditions. Therefore, I am looking for a 
suitable summary measure of the response bias.

In principle, I could compute c or c-sub-a for each point on the ROC 
curve and then use the arithmetic mean of these three values as my 
summary measure. The problem is, however, that occasionally some 
listeners did not use all of the four rating categories, so that I have 
to collapse categories. And it is of course a problem to compare mean(c) 
for an ROC with 3 points to mean(c) for an ROC curve with 2 points.

Any suggestions as to a good way to summarize bias or to test for 
differences in response bias in this situation would be highly 
appreciated...

For example, I could imagine that one could use a proportional-odds 
logistic regression model to see whether the experimental condition had 
an effect on the probability of a positive response, but I never came 
across a paper where this method was used.

Kind regards,

Daniel

--
Dr. Daniel Oberfeld-Twistel
Johannes Gutenberg - Universitaet Mainz
Department of Psychology
Experimental Psychology

Staudingerweg 9
55128 Mainz
Germany

Phone ++49 (0) 6131 39 22423
Fax   ++49 (0) 6131 39 22480
http://www.staff.uni-mainz.de/oberfeld/