Pragmatics of Pooling in ANOVA Tables

Pragmatically, is “pooling” worth doing in analysis of variance (ANOVA) tables, statistical niceties aside? The conditions found for pooling to be even potentially rewarding are more restrictive than might be expected, and power improvements are generally poor. Using only elementary arguments and calculations with popular spreadsheets, analyses of standard simple cases show two in which pooling is possibly both sensible and of practical potential benefit: Pooling across sources and pooling of highest and next-to-highest order interaction terms as an error term in the unreplicated 2n design case. The special case of paired or unpaired t tests is also examined, and the sample correlation needed to make the paired t test more powerful than the unpaired one is found to be both low and well below conventionally statistically significant values.