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Let us assume that for each of subject there exist two measurements obtained under different conditions , and that we are interested in the significance of the mean group difference
. We will assume that the between-subject variance and the between-session variance is equal across subjects and conditions. Note that this is a notational simplification within this framework which might or might not become a necessary condition once we try to estimate the associated group-level parameters.
Similar to the previous sections, we model this as

and

Let
where, again,
and where the group design matrix,
, de-means the first level estimates for each subject. Assume for simplicity that
,
and define
. Then
will be block diagonal with blocks of
Furthermore, let
and
. Then
so that

Using
, the group parameter estimate writes as
As expected, the variance of the group level estimate no longer depends on the between-subject variance
. Note that this approach is equivalent to using a three level approach with an unpaired -test of de-meaned repeated measures.

**Subsections**

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Christian Beckmann
2003-07-16