a tricky question on probabilities

Hi,

I have a tricky question to which people at work have no answer.

I have some participants localising sounds in azimuth. There are 12 speakers
all around them, level with with ears. A speaker makes a noise and the
subject indicates from which speaker they believe the sound was presented.
Subjects do a large number of trials (over 1000). So I have lots of data.

My subjects are deaf in one ear. Can't hear at all from that ear. Somewhat
unsurprisingly, they get more correct responses on their hearing side than
their non-hearing side. i.e. the proportion of trials (localisation
judgements) which are correct is higher on the hearing side. HOWEVER, if I
count up the total number of responses they make to the hearing and
non-hearing sides, I find that subjects make 10-20% more responses to
speakers on the side from which they can hear. Their responses are biased.
So the higher performance on the hearing side is, to an extent, due to the
fact that subjects make more responses in this direction.

I would like to address the following question: is performance on the
hearing side is more accurate than on the non-hearing side? In other words,
having accounted for the bias, are there still more correct responses on
the hearing side? Clearly, to answer this I need a test that takes response
bias into account. That is where I'm stuck. Is a Bayesian approach (a topic
about which I know nothing) the solution?


Any suggestions gratefully received,
Rob

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