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We considered the linear one- way repeated measurements model which has only one within units factor and one between units factor incorporating univariate random effects as well as the experimental error term. A Bayesian approach based on Markov Chain Monte Carlo (MCMC) is employed to mak inferences on the one- way repeated measurements model. Furthermore, the Bayesian approach to the one-way repeated measurement model is described after representing the model as a mixed model. We investigated the asymptotic properties of the Bayes factor for testing the fixed effects linear one- way repeated measurements model against the mixed one- way repeated measurements alternative model., we identified the analytic form of the Bayes factor and showed that, the Bayes factor is consistent. To illustrate the effectiveness of our methodology, we have chosen the data set of an experiment conducted during a winter of 2008-2009 in order to investigate the effect of calcium on growth, the yield ofcultivars of cucumber and the storage temperature on storage capability and quality. Another set of data was chosen from a study conducted at a university of Basrah.
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