A Constructive Procedure for Unbiased Controlled Rounding

Abstract It is often necessary to round values in a two-way statistical table, that is, replace each value by an adjacent integer multiple of an appropriately chosen integer rounding base. Such is the case when statistical data are to be presented in increments, such as personal income presented in multiples of $1,000 or retail sales in units of $1 million, or when counts must be adjusted prior to release to reduce the risk of statistical disclosure (Cox, McDonald, and Nelson 1986). It is desirable that the rounded array also be additive along rows and columns and to the grand total. A table satisfying these conditions is called a controlled rounding of the original table. If, as is often the case, entries that are already integer multiples of the base must remain unchanged, the controlled rounding is said to be zero-restricted. Controlled rounding is an important adjunct to statistical methods for adjusting contingency tables such as iterative proportional fitting (Ireland and Kullback 1968), because suc...