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Bayesian Statistics: An Introduction, 4th Edition by Peter M. Lee

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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

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from I independent populations with, however, a common variance  . For simplicity, we shall assume independent reference priors uniform in  and  , that is

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The likelihood is

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where

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and so the posterior ...

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