The Impact of Cell Adjustment on the Analysis of Aggregate Census Data

Cell adjustment involves the random perturbation of tabular counts by statistical agencies, prior to publication, in order to minimise the risks of disclosing confidential information about individual survey respondents. A variety of cell adjustment regimes have been applied to past and present census outputs. For each a method of estimating the confidence interval associated with the aggregation of potentially perturbed counts is presented. In this paper I also investigate the impact that alternative cell adjustment regimes have on a variety of standard user analyses—ranging from the summation of cell counts through to the ranking of areas and the fitting of multivariate regression models—including, in addition, the effects of geographical aggregation. The conclusion of the paper is that the choice recently offered to UK census users between the current methods of cell adjustment adopted in New Zealand and those adopted in Australia is finely balanced and analysis specific. What is clear is that both methods have a significant adverse impact on a range of analyses—in particular, the ranking of areas. In consequence, a case is advanced for abandoning cell adjustment, or, at the very least, for publishing independently adjusted counts for all table marginals. Finally, advice is offered to users on minimising the impact of cell adjustment on their analyses.