Interval Estimation of Population Proportion in a Double Sampling Scheme

이중표본에서 모비율의 구간추정

Lee, Seung-Chun;Choi, Byong-Su

  • Received : 20090800
  • Accepted : 20091000
  • Published : 2009.12.31


The double sampling scheme is effective in reducing the sampling cost. However, the doubly sampled data is contaminated by two types of error, namely false-positive and false-negative errors. These would make the statistical analysis more difficult, and it would require more sophisticate analysis tools. For instance, the Wald method for the interval estimation of a proportion would not work well. In fact, it is well known that the Wald confidence interval behaves very poorly in many sampling schemes. In this note, the property of the Wald interval is investigated in terms of the coverage probability and the expected width. An alternative confidence interval based on the Agresti-Coull's approach is recommended.


False-positive error;false-negative error;Wald confidence interval;Agresti-Coull confidence interval;coverage probability


  1. 이승천 (2006). 독립표본에서 두 모비율 차이에 대한 가중 Polya 사후분포 신뢰구간, <응용통계연구>, 19, 171–181
  2. 이승천 (2007). 베이지안 접근에 의한 모비율 선형함수의 신뢰구간, <응용통계연구>, 20, 257–266
  3. Agresti, A. and Coull, B. A. (1998). Approximation is better than 'exact' for interval estimation of binomial proportions, American Statistician, 52, 119–126
  4. Agresti, A. and Caffo, B. (2000). Simple and effective confidence intervals for proportions and differences of proportions result from adding two successes and two failures, American Statistician, 54, 280–288
  5. Agresti, A. and Min, Y. (2005). Simple improved confidence intervals for comparing matched proportions, Statistics in Medicine, 24, 729–740
  6. Boese, D. H., Young, D. M. and Stamey, J. D. (2006). Confidence intervals for a binomial parameter based on binary data subject to false-positive misclassification, Computational Statistics and Data Analysis, 50, 3369–3385
  7. Braunstein, G. (2002). False-positive serum human chronic gonadotropin results: causes, characteristics, and recognition, American Journal of Obstetrics & Genecology, 187, 217–224
  8. Bross, I. (1954). Misclassification in tables, Biomometrics, 10, 478–486
  9. Brown, L. D., Cai, T. T. and DasGupta, A. (2001). Interval estimation for a binomial proportion, Statistical Science, 16, 101–133
  10. Kazemi, N., Dennien, B. and Dan, A. (2001). Mistaken identity: A case of false positive on CT angiography, Journal of Clinical Neuroscience, 9, 464–466
  11. Lee, S.-C. (2006). Interval estimation of binomial proportions based on weighted Polya posterior, Computational Statistics and Data Analysis, 51, 1012–1021
  12. Lee, S.-C. (2007). An improved confidence interval for the population proportion in a double sampling scheme subject to false-positive misclassification, Journal of the Korean Statistical Society, 36, 275–284
  13. Price, R. M. and Bonett, D. G. (2004). An improved confidence interval for a linear function of binomial proportions, Computational Statistics and Data Analysis, 45, 449–456
  14. Raats, V. M. and Moors, J. J. A. (2003). Double-checking auditors: A Bayesian approach, Statistician, 52, 351–365
  15. Swaen, V. M., Teggerler, O. and Amelsvoort, L. (2001). False positive outcomes and design characteristics in occupational cancer epidemiology studies, International Journal of Epidemiology, 30, 948–955
  16. Tenenbein, A. (1970). A double sampling scheme for estimating from binomial data with misclassifications, Journal of the American Statistical Association, 65, 1350–1361
  17. Tenenbein, A. (1971). A double sampling scheme for estimating from binomial data with misclassifications: sample size determination, Biometrics, 27, 935–944
  18. Tenenbein, A. (1972). A double sampling scheme for estimating from multinomial data with application to sampling inspection, Technometrics, 14, 187–202
  19. York, J., Madigan, D., Heuch, I. and Lie, R. T. (1995). Birth defects registered by double sampling: a Bayesian approach incorporating covariates and model uncertainty, Applied. Statistics, 44, 227–242

Cited by

  1. Theoretical Considerations for the Agresti-Coull Type Confidence Interval in Misclassified Binary Data vol.18, pp.4, 2011,
  2. Bayesian confidence intervals of proportion with misclassified binary data vol.42, pp.3, 2013,


Supported by : 한국학술진흥재단