Abstract
In a one-way random model, the variance of the sample mean is estimated by the between-group mean squares divided by the total number of observations. If there is no group differences, it is advantageous to pool the within-group mean squares with the between-group mean squares. When it is uncertain whether the groups are different, a preliminary test may be used. A preliminary test estimator of the variance is given and its bias and mean square error are derived. Recommendation of the level of the preliminary test is given.
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