Sweeping,alignment and the analysis of unbalanced data

The terms sweeping and alignment refer to the same process. Sweeping/alignment is used by data analysts as a technique for describing the effects of a model factor (e.g., treatments in a randomized block design) after the effects of nuisance parameters (e.g., blocks) have been removed from the data. In this paper sweeping/alignment is used as the basis for developing tests of factors in unbalanced experimental design models. Formulas are presented for treatment effects in randomized block designs with missing observations, and for interaction and main effects in unbalanced two-way factorial designs with empty cells.