Comparing means - 2 repeated measures variables, controlling for covariate with heterogeneous slope

I have a 2 level repeated measures DV of accuracy, and a covariate of response bias. As response bias increases, accuracy level 1 increases while level 2 decreases. I want to see if there is a difference in the means of the groups after controlling for response bias.

I can't do it with an ANCOVA. Can I just manually calculate expected values based on a regression equation, and run an ANOVA?

I'd like to do it in R or SPSS, so specifics for either would be welcome, but not necessary.

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It's hard to tell for sure, but your situation sounds a lot like signal detection theory. You may want to look into that. If you could extract d' for each unit, you will have a measure of accuracy separated from response bias. – gung Sep 6 '12 at 16:27
You're right! I ruled out SDT a while ago because I only had my two accuracy measures, but then worked out a way to get the reponse bias measure and didn't consider it properly again. Curious to see how it compares to the below suggestion... – Charlie Sep 7 '12 at 0:31
I can't quite follow your questions? Does "accuracy level 1 and accuracy level 2" mean just two measurement for different kind of accuracy? Or is it that the level 2 accuracy is the group accuracy that only differs from group to group? I think for SDT, we only need 1-FAR and HIT rate, two different accuracy, at least for basic SDT model. Can you elaborate your question and how you pulled it out? – KH Kim Oct 15 '12 at 11:20
each participant had one accuracy score for stimulus x and one for stimulus y. While I believe SDT would work, and may use it if I go back to the data, I ended up using observed response bias of each participant to calculate a 'response bias predicted' accuracy score for each accuracy score, then subtracted that from the observed accuracy scores. this left me with the improvement in accuracy not attributable to response bias, (but with a fair bit of error) and I compared these in a repeated measures anova. – Charlie Oct 15 '12 at 23:29