Effects of Rounding Continuous Data Using Specific Rules

• Activity Number: 441
• Type: Contributed
• Date/Time: Thursday, August 12, 2004 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Joe Fred Gonzalez, Jr.*+ and Jay J. Kim and Lawrence H. Cox and Myron Katzoff
• Companies: National Center for Health Statistics and National Center for Health Statistics and National Center for Health Statistics and National Center for Health Statistics
• Keywords: rounding ; integer ; variance ; uniform distribution ; disclosure risk ; posterior probability

Abstract

Data such as incomes are frequently rounded. Rounding may be done to protect the confidentiality of records in a file or to enhance readability of the data, or by the notion that the digits subject to rounding are inconsequential. The rounding may not have any effect on the bias of an estimator, but may have a large impact on variance. Integers can be expressed as x=qB+r, where q is the quotient, B is the base, and r is the remainder. B is a constant, but q and r are random variables. We use four rules for rounding "r" above to observe the effects of rounding on bias and variance. We will assume a uniform distribution on r, but no specific distributional assumption will be made on "q." When q =0, we will show that the variance after rounding is three times the variance before rounding. As the variance of q gets larger, the effect of rounding on the variance decreases. Disclosure risk in terms of the posterior probability P(x|qB) will also be shown.