Re: a tricky question on probabilities

Rob Campbell wrote:
> 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
>
> --
> remove ferret to reply

The usual Pearson chi-square test of independence on a subject's
12 x 12 contingency table (row = stimulus, column = response)
would be one way of checking to see if that subject's responses
might be related to the stimuli.

.

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