6.5 Comparison of several means – the one way model
6.5.1 Description of the one way layout
Sometimes we want to compare more than two samples. We might, for example, wish to compare the performance of children from a number of schools at a standard test. The usual model for such a situation is as follows. We suppose that 
is a vector of unknown parameters and that there are 
independent observations
from I independent populations with, however, a common variance 
. For simplicity, we shall assume independent reference priors uniform in 
and 
, that is
The likelihood is
where
and so the posterior ...
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