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I would like to know whether z-standardization is an appropriate way to account for a covariate. Please consider the following dummy example (I am not interested in the interpretation of the result but only in the statistical plausibility):

In a sample of 100 subjects relationship between IQ and head size is investigated (one measurement per subject). However IQ has been estimated with IQ Test 'A' in some subjects and with IQ test 'B' in the other subjects. Also there is a significant difference in IQ measured by 'A' as compared to IQ measured by 'B'. Therefore 'zIQ' is obtained by z-standardization of all IQ values obtained by test 'A' as well as z-standardization of all IQ values obtained by 'B'. Is it appropriate to use zIQ to investigate its relationship with head size independently of which test ('A' or 'B') has been used?

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Why did some people get test A and some test B? In general, test equating for this type of test is pretty complex, and just z-transforming won't do it. – Peter Flom Sep 21 '12 at 11:26
It is a dummy example. However I think it often occurs that 'merged datasets' need to be analyzed in which several samples (e.g. from different centers) were put together and therefore adjusting for covariates might be necessary. – jokel Sep 21 '12 at 11:30
If it is data from several different centers, then you probably need a multilevel model. – Peter Flom Sep 21 '12 at 11:45
Sometimes people just model the centers as random effects. – Michael Chernick Sep 22 '12 at 15:51

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