This paper presents a predictive approach to the random effect model, comparing two Bayesian methods for estimating treatment means. The first method, the fixed effect model, uses the sample mean as an estimator, while the second, the random effect model, uses a weighted combination of the treatment mean and the grand mean. Both methods are justified from a Bayesian perspective with different prior distributions. The random effect model is derived from a hierarchical normal model with normal priors for the treatment means. The paper discusses the use of predictive distributions for new observations and the estimation of the weighting coefficient μ. The paper proposes two methods for evaluating the weighting coefficient μ. Method I involves omitting one observation from each group and computing the mean squared prediction error. Method II involves simultaneously omitting one observation from each group and computing the squared deviation of the predicted value from the actual value. Both methods lead to expressions for the mean squared prediction error, which can be minimized to find the optimal μ. The paper also discusses the mixed model case, where both fixed and random effects are present. It shows that the methods can be extended to this case and that the optimal μ can be found by minimizing the mean squared prediction error. The paper concludes that both methods yield very close estimates for the weighting coefficient and that the mean squared prediction error is relatively flat near its minimum. This suggests that the methods are robust to variations in the weighting coefficient. The paper also notes that Lindley's Bayesian procedure for this type of data is not easily computable due to the need for arbitrary prior assignments. The paper concludes that the proposed methods are useful for estimating treatment means and that they are relatively free of distributional assumptions.This paper presents a predictive approach to the random effect model, comparing two Bayesian methods for estimating treatment means. The first method, the fixed effect model, uses the sample mean as an estimator, while the second, the random effect model, uses a weighted combination of the treatment mean and the grand mean. Both methods are justified from a Bayesian perspective with different prior distributions. The random effect model is derived from a hierarchical normal model with normal priors for the treatment means. The paper discusses the use of predictive distributions for new observations and the estimation of the weighting coefficient μ. The paper proposes two methods for evaluating the weighting coefficient μ. Method I involves omitting one observation from each group and computing the mean squared prediction error. Method II involves simultaneously omitting one observation from each group and computing the squared deviation of the predicted value from the actual value. Both methods lead to expressions for the mean squared prediction error, which can be minimized to find the optimal μ. The paper also discusses the mixed model case, where both fixed and random effects are present. It shows that the methods can be extended to this case and that the optimal μ can be found by minimizing the mean squared prediction error. The paper concludes that both methods yield very close estimates for the weighting coefficient and that the mean squared prediction error is relatively flat near its minimum. This suggests that the methods are robust to variations in the weighting coefficient. The paper also notes that Lindley's Bayesian procedure for this type of data is not easily computable due to the need for arbitrary prior assignments. The paper concludes that the proposed methods are useful for estimating treatment means and that they are relatively free of distributional assumptions.