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Pooling

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Definition

When a designed experiment is used to evaluate a large number of factor effects of which just a few are significant, the insignificant ones may be assumed negligible and combined or ‘pooled’ into the error estimate. The pooling process involves adding the sums of squares and Degrees of Freedom for the insignificant effect(s) into the Error term. This implies that the variance for the pooled effect(s) is not larger than the variance associated with the Error.

Provided that the pooled effects really are insignificant (we did not commit a Type II error), we have much to gain by doing this because it increases the degrees if freedom for error, improving the precision of further tests. However, if one or more of the pooled effects really are significant, then the resulting error sum of squares may be over-inflated, making other significant effects harder to detect.

One practical approach is to pool only if the original error degrees of freedom are less than six and the effect to be pooled is not significant at a large value of alpha, such as alpha = 0.25.1

1Design and Analysis of Experiment (5th Ed.), Douglas C. Montgomery

External Links

More on the Effects of Pooling, from Tufts University: - http://www.tufts.edu/~gdallal/pool.htm