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## Unpaired Group Difference

We assume that the individual subjects are grouped in two groups and that within each group the first-level parameters are normally distributed around a group-specific mean. That is and In order to simplify further notation and without loss of generality we assume that the subjects belong to the first group and subjects belong to the second group. We do not make any assumption about the first-level covariance structure and simply set Then is block diagonal with elements If we define and , the group parameter estimate writes as       where the variance, as usual, is calculated from the first term as Under the same assumptions as before, of equal covariance at the first level and normalised designs (i.e. homoscedastic model), these equation simplify to and thus with Note that the second level contrast includes an appropriate scaling constant. This factor becomes irrelevant once the group parameter of interest is combined with its variance to form a test statistic.

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Christian Beckmann 2003-07-16