A new method for adjusting a frequency table to fixed marginal totals by the reconstitution formula of correspondence analysis

The problem of adjusting a frequency table to fixed marginal totals is considered. Two distinct methodological approaches to this problem exist in the literature. The first one consists in minimizing some dissimilarity criterion under the constraint that the marginal totals remain fixed. The second one resorts to the reconstitution formula of factorial correspondence analysis in order to reconstruct a table with the desired marginal totals. This latter approach is briefly reviewed and a new adjustment method is proposed which enjoys intuitively appealing invariance properties: invariance of the contingency phi-square value, hence preservation of the independence situation, reversibility of the adjustment. Moreover, it provides a straightforward determination of the factorial correspondence analysis co-ordinates of the reconstructed table.