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Balancing - Analysis of Variance by Another Name

In Report 7 (1971) of the National Assessment of Educational Progress, an analytic technique known as balancing was introduced. The stated purpose of this technique is the elimination of confounding in multifactor survey studies in which some attributes are not equally represented in all cells of the survey sample design. The likely impact of the NAEP reports is great, and it is vital that the nature of the analyses and their relationships to other known analytic techniques be clearly understood. This report shows that the estimation procedure used in balancing is the equivalent of that employed in the nonorthogonal analysis of variance in an additive model. The nature of weighting schemes for the definition of marginal populations is considered in detail as well as the implications of these various schemes to interpretation of results. The results on weighting schemes and interpretations apply to both balancing and a much broader class of analyses.