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Background:

I have two groups of children - one group with normal hearing and one with permanent hearing losses - call them NH and PHL.

Each child has had a hearing test, consisting of 6 different sounds (.25, .5, 1, 2, 4, and 8KHz) assessed under three different test conditions (classic, remote, and hybrid)

Each child therefore has 18 data points - three conditions by six sounds.

Questions:

How can I test the hypothesis that, for each of the six sounds, the three test conditions returned the same hearing thresholds and that there is no difference between the groups in this respect?

That is, both normal hearing and hearing impaired children generated the same hearing test results in the three test conditions. I am not interested in the actual differences in hearing levels between the groups as I already know how well they hear - I just need to know that their hearing levels are the same no matter how I test them.

If there are differences between the groups or between the conditions, how can I examine the interaction effects to see whether the differences were greatest for particular sounds or in particular conditions?

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What is your specific question? – Aniko Jun 7 '12 at 13:04
your problem it is not clear, but it is nice to star a discussion. I would think in a factorial ANOVA, using groups (with two levels), sounds (6 levels) and test condition (3 levels). However you are having problems with the independence assumption since your are measuring a response variable on the same child, so the correct model is more complex. How is the nature of the response variable ordinal? or quantitative?, – Damian Jun 8 '12 at 1:19

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