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Journal of Applied Mathematics
Volume 2014, Article ID 738097, 6 pages
Research Article

Sample Size Determination for the Polychotomous Randomized Response Model for Sensitive Questions in a Stratified Two-Stage Sampling Survey

1School of Public Health, Medical College of Soochow University, Suzhou 215123, China
2Department of Mathematics, Dezhou University, Dezhou 253023, China
3Changzhou No. 2 People’s Hospital, Changzhou 213003, China

Received 1 August 2013; Revised 12 March 2014; Accepted 18 March 2014; Published 22 April 2014

Academic Editor: Ch. Tsitouras

Copyright © 2014 Zongda Jin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Methods of finding the minimum value and the Lagrange function were applied to deduce the formulae for the optimum sample sizes for polychotomous randomized response technique (RRT) model in stratified two-stage sampling, so as to minimize the cost for specified sampling errors and to minimize the sampling errors under the constraint of a fixed budget. These formulae were successfully applied to sensitive topics survey among men who have sex with men (MSM) in Beijing, China.