Fast Calculation of Exact Contingency Table Cell Bounds Given Conditional Frequencies

• Activity Number: 89
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 4:00 PM to 5:50 PM
• Sponsor: Government Statistics Section
• Author(s): Byran Smucker*+ and Steven Wright and Andrew Sage
• Companies: Miami University and Miami University and Miami University
• Keywords: Confidentiality ; Contingency tables ; Integer programming ; Knapsack ; Statistical disclosure control ; Cell bounds

Abstract

For a contingency table, we consider the bounds on the underlying cell counts that can be deduced if unrounded conditional probabilities and sample size are released. This is a problem that has implications for statistical disclosure limitation, and we reformulate the standard integer programming approach as a knapsack problem, which reduces computational requirements drastically. We also introduce results that give closed form bounds in certain cases and present conditions that result in the full disclosure of the tabular counts. We consider several different datasets illustrating our approach.