Abstract
Eichhorn and Hayre (J Stat Plan Inference 7:307–316, 1983) introduced the scrambled response technique to gather information on sensitive quantitative variables. Singh and Joarder (Metron 15:151–157, 1997), Gupta et al. (J Stat Plan Inference 100:239–247, 2002) and Bar-Lev et al. (Metrika 60:255–260, 2004) permitted the respondents either to report their true values on the sensitive quantitative variable or the scrambled response and developed the optional randomized response (ORR) technique based on simple random sample with replacement (SRSWR). While developing the ORR procedure, these authors made the assumption that the probability of disclosing the true response or the randomized response (RR) is the same for all the individuals in a population. This is not a very realistic assumption as in practical survey situations the probability of reporting the true value or the RR generally varies from unit to unit. Moreover, if one generalizes the ORR method as developed by these authors relaxing the ‘constant probability’ assumption, the variance of an unbiased estimator for the population total or mean can not be estimated as this involves the unknown parameter, ‘the probability of revealing the true response’. Here we propose a modified ORR procedure for stratified unequal probability sampling after relaxing the assumption of ‘constant probability’ of providing the true response. It is also demonstrated with a numerical exercise that our procedure produces better estimator for a population total than that provided by the method suggested by the earlier authors.
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Bar-Lev SK, Bobovitch E, Boukai B (2004) A note on randomized response models for quantitative data. Metrika 60: 255–260
Chaudhuri A, Mukerjee R (1985) Optionally randomized response techniques. Cal Stat Assoc Bull 34: 225–229
Chaudhuri A, Mukerjee R (1988) Randomized response: theory and techniques. Marcel Dekker Inc, New York
Chaudhuri A, Saha A (2005) Optional versus compulsory randomized response techniques in complex surveys. J Stat Plan Inference 135: 516–527
Christofides TC (2005) Randomized response in stratified sampling. J Stat Plan Inference 128(1): 303–310
Eichhorn BH, Hayre LS (1983) Scrambled randomized response method for obtaining sensitive quantitative data. J Stat Plan Inference 7: 307–316
Eriksson SA (1973) A new model for randomized response. Int Stat Rev 41: 40–43
Greenberg BG, Abul-ela AL, Simmons WR, Horvitz DG (1969) The unrelated question randomized response model: theoretical frame work. J Am Stat Assoc 64: 520–539
Gupta S, Gupta B, Singh S (2002) Estimation of sensitivity level of personal interview survey questions. J Stat Plan Inference 100: 239–247
Horvitz DG, Shah BV, Simmons WR (1967) The unrelated question randomized response model. In: Proc. Soc. Sec. Amer. Stat. Assoc, pp 65–72
Kim JM, Warde WD (2004) A stratified Warner’s randomized response model. J Stat Plan Inference 120: 155–165
Raj Des (1968) Sampling theory. McGraw-Hill, New York
Rao JNK, Hartley HO, Cochran WG (1962) On a simple procedure of unequal probability sampling without replacement. J Roy Stat Soc B 24: 482–491
Saha A (2004) On efficacies of Dalenius-Vitale Technique with Compulsory versus Optional Randomized Responses from Complex Surveys. Cal Stat Assoc Bull 54: 223–230
Singh S, Joarder AH (1997) Optional randomized response technique for sensitive quantitative variable. Metron 15: 151–157
Warner SL (1965) Randomized response: a survey technique for eliminating evasive answer bias. J Am Stat Assoc 60: 63–69
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Saha, A. An optional scrambled randomized response technique for practical surveys. Metrika 73, 139–149 (2011). https://doi.org/10.1007/s00184-009-0269-9
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DOI: https://doi.org/10.1007/s00184-009-0269-9