An Efficient Survey Technique for Estimating the Proportion and Sensitivity Attributes in a Dichotomous Finite Population

  • Amod KumarEmail author
  • G. N. Singh
  • Gajendra K. Vishwakarma
Research Article


In this paper, a simple survey technique is applied to estimate the population proportion π of a sensitive trait, in addition to T, the probability that a respondent truthfully states that he or she bears a sensitive character when questioned directly and examined its properties. It has been found that the suggested model is efficient. Numerical illustrations are presented to support the theoretical results.


Randomized response Direct response Estimation of proportion Privacy and sensitive attributes 

Mathematics Subject Classification



  1. 1.
    Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60:63–69CrossRefGoogle Scholar
  2. 2.
    Greenberg B, Abul-Ela A, Simmons WR, Horvitz DG (1969) The unrelated question randomized response model: theoretical framework. J Am Stat Assoc 64:529–539MathSciNetGoogle Scholar
  3. 3.
    Moors JJA (1971) Optimization of the unrelated question randomized response model. J Am Stat Assoc 66(335):627–629CrossRefGoogle Scholar
  4. 4.
    Lanke J (1976) On the degree of protection in randomized interview. Int Stat Rev 44(2):80–83MathSciNetCrossRefGoogle Scholar
  5. 5.
    Fox JA, Tracy PE (1986) Randomized response: a method of sensitive surveys. SAGE, Newbury ParkCrossRefGoogle Scholar
  6. 6.
    Mangat NS, Singh R (1990) An alternative randomized procedure. Biometrika 77:439–442MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ryu JB, Hong KH, Lee GS (1993) Randomize response model. Freedom Academy, SeoulGoogle Scholar
  8. 8.
    Mangat NS (1994) An improved randomized response strategy. J R Stat Soc B 56(1):93–95MathSciNetzbMATHGoogle Scholar
  9. 9.
    Singh S, Singh R, Mangat NS, Tracy DS (1995) An improved two-stage randomized response strategy. Stat Pap 36:265–271MathSciNetCrossRefGoogle Scholar
  10. 10.
    Mahmood M, Singh S, Horn S (1998) On the confidentiality guaranteed under randomized response sampling: a comparison with several new techniques. Biom J 40:237–242MathSciNetCrossRefGoogle Scholar
  11. 11.
    Singh S, Singh R, Mangat NS (2000) Some alternative strategies to Moor’s model in randomized response model. J Stat Plan Inference 83:243–255MathSciNetCrossRefGoogle Scholar
  12. 12.
    Chang HJ, Huang KC (2001) Estimation of proportion and sensitivity of a qualitative character. Metrika 53:269–280MathSciNetCrossRefGoogle Scholar
  13. 13.
    Huang KC (2004) Survey technique for estimating the proportion and sensitivity in a dichotomous finite population. Stat Neerl 58:75–82MathSciNetCrossRefGoogle Scholar
  14. 14.
    Kim JM, Warde WD (2005) A mixed randomized response model. J Stat Plan Inference 133:211–221MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kim JM, Elam ME (2005) A two-stage stratified Warner’s randomized response model using optimal allocation. Metrika 61:1–7MathSciNetCrossRefGoogle Scholar
  16. 16.
    Ryu JB, Kim JM, Heo TY, Park CG (2005–2006) On stratified randomized response sampling. Model Assist Stat Appl 1:31–36Google Scholar
  17. 17.
    Hong Z (2005–2006) Estimation of mean in randomized response surveys when answers are incompletely truthful. Model Assist Stat Appl 1:221–230Google Scholar
  18. 18.
    Perri PF (2008) Modified randomized devices for simmon’s model. Model Assist Stat Appl 3(3):233–239MathSciNetzbMATHGoogle Scholar
  19. 19.
    Singh HP, Tarray TA (2013) A modified survey technique for estimating the proportion and sensitivity in a dichotomous finite population. Int J Adv Sci Tech Res 6(3):459–472Google Scholar
  20. 20.
    Tracy DS, Osahan SS (1999) An improved randomized response technique. Pak J Stat 15:1–6MathSciNetzbMATHGoogle Scholar

Copyright information

© The National Academy of Sciences, India 2019

Authors and Affiliations

  • Amod Kumar
    • 1
    Email author
  • G. N. Singh
    • 1
  • Gajendra K. Vishwakarma
    • 1
  1. 1.Department of Applied MathematicsIndian Institute of Technology (ISM) DhanbadDhanbadIndia

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