In engineering experiments, `Sometimes Pooling Rules` to remove insignificant terms from the model has been implemented to increase the power of detecting the small size of main effects when the preliminary test of higher order interaction effects declare to be insignificant. In this note, we review the sometimes pooling rules in the literature and also study the probability of the length of 95% confidence interval of of the comparison of two independent samples being shorter than that of the paired comparison at the various level of significance of the preliminary test and the insufficient number of blocks n in [2,13], given the block effects being pooled to the error term. This study supports that the sometimes pooling results in the power improvement of the main effects.
Sometimes pooling rules;level of significance of the preliminary test;comparison of two independent samples;paired comparison;
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