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We proposed three methods to find an approximate confidence interval for the variance of the random effects for a one-way analysis of the variance model in completely randomized design. We compared the proposed methods with some other methods reported in the literature. Several criteria are used for the empirical comparisons: the mean width of the confidence interval, the variance of the width, and the coverage probability. We use Simulation and Monte-Carlo techniques to perform the comparison study. We use R language to facilitate the simulation procedures. We found that one of the proposed methods was in general superior to the others.
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