Making Tables Additive in the Presence of Zeros

SYNOPTIC ABSTRACTGiven a two-way contingency table of non-negative rational numbers in which the internal entries do not sum to the corresponding marginals, there is often the need to adjust internal entries to achieve additivity. In general, the objective is to have the revised table close, in some sense, to the original table and to have zero entries remain zero and positive entries remain positive. Not all two-way contingency tables can be adjusted to achieve additivity subject to the constraints above. In this paper we present a procedure that will determine whether a given table can be so adjusted.