Abstract #302160

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JSM 2003 Abstract #302160
Activity Number: 170
Type: Contributed
Date/Time: Monday, August 4, 2003 : 2:00 PM to 3:50 PM
Sponsor: Section on Survey Research Methods
Abstract - #302160
Title: Stratum Boundaries and Sample Allocation in Special Ratio-Type Data
Author(s): Mary K. Batcher*+ and Yan Liu
Companies: Ernst & Young and Ernest and Young
Address: 2502 N Gate Terrace, Silver Spring, MD, 20906-2235,
Keywords: mixture distributions ; audit sampling ; stratified sampling ; Neyman allocation ; ratio estimation
Abstract:

Auditors are often faced with reviewing a sample drawn from special populations where ratio-type estimation is appropriate. The population of invoices is divided into two categories according to whether or not the invoices meet certain requirements. In other words, the correct amount follows a nonstandard mixture distribution in which the correct amount is either zero with a certain probability or the same as the original invoice amount with a certain probability. Under this scenario, the typical sample design is the stratified random sample and the estimation method is the ratio-type method. We analyze the determination of stratum boundaries and the allocation of sample size under this special population. Roberts's formula is compared to the standard ratio formula. We also study the special population with some invoices partially qualified, i.e., the correct amount is a portion of the invoice amount. In this paper, we analyze the application of Roberts's formula by investigating the bias and variance estimate.

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