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Summarizing response bias in a detection experiment using the rating method

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,


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

Staudingerweg 9
55128 Mainz

Phone ++49 (0) 6131 39 22423
Fax   ++49 (0) 6131 39 22480