Indirect Questioning Technique Related to Sensitive Quantitative Variables with Options for Direct, Randomized and Item Count Responses

International Journal of Statistical Sciences Pub Date : 2024-03-28 DOI:10.3329/ijss.v24i1.72035

Purnima Shaw, Sanghamitra Pal

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Abstract

Randomized Response (RR) Technique (RRT) pioneered by Warner (1965) is a useful tool to elicit responses on sensitive characteristics, such as induced abortions, drug abuse, drunken driving, total amount of counterfeit notes of a particular denomination held by individuals in the population, etc. There exists a huge literature on Randomized Response (RR) devices for estimation of finite population mean of quantitative variables, sensitive in nature mostly based on Eichhorn and Hayre (1983). Device-I and Device-II vide Chaudhuri and Christofides (2013) allow estimation of population mean of sensitive quantitative variables using sample chosen by a general sampling design. On the other hand, Item Count Technique (ICT), described elaborately in Chaudhuri and Christofides (2013), is an alternative to RRT for respondents who do not choose to provide RRs. While some respondents may find a variable as sensitive, others may find it innocuous enough to provide a direct response (DR) about his/her true value. In such a case, Optional Randomized Response (ORR) Technique (ORRT) with options for DR and RR was introduced by Chaudhuri and Mukherjee (1985). Pal (2007) proposed an ORR device which offers choices for RR and ICT to the respondents for giving their answers. A new ORRT with options for DR, RR and ICT was provided by Shaw and Pal (2021) for eliciting indirect responses on sensitive characteristics. As this device relates to estimation of population proportion of sensitive characteristics, an attempt has been made to extend it for sensitive quantitative variables. Further, to take care of individuals’ varying choices for DR, RR and ICT and to protect the privacy of the respondents’ choices, this paper develops an ORR device allowing the respondents chosen by a general sampling design, to choose any one of the three options according to their choices. International Journal of Statistical Sciences, Vol.24(1), March, 2024, pp 155-170

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与敏感定量变量有关的间接提问技术，可选择直接回答、随机回答和项目计数回答

华纳（Warner，1965 年）首创的随机反应技术（RRT）是一种有用的工具，可用于诱导对敏感特征的反应，如人工流产、药物滥用、醉酒驾驶、人口中个人持有的特定面值假钞总量等。目前有大量关于随机反应（RR）装置的文献，用于估算定量变量的有限人口平均值，这些敏感变量大多基于 Eichhorn 和 Hayre（1983 年）。通过 Chaudhuri 和 Christofides（2013 年）的 Device-I 和 Device-II，可以使用一般抽样设计选择的样本估算敏感定量变量的总体均值。另一方面，Chaudhuri 和 Christofides（2013 年）详细介绍的项目计数技术（ICT）是 RRT 的替代方法，适用于不选择提供 RRs 的受访者。有些受访者可能认为某个变量很敏感，而有些受访者则可能认为该变量很无害，可以直接回答（DR）其真实值。在这种情况下，Chaudhuri 和 Mukherjee（1985 年）提出了具有 DR 和 RR 选项的可选随机响应技术（ORRT）。Pal（2007 年）提出了一种 ORR 装置，为受访者提供 RR 和 ICT 选项，以便他们给出答案。Shaw 和 Pal（2021 年）提供了一种新的 ORRT，其中包含 DR、RR 和 ICT 选项，用于诱导对敏感特征的间接回答。由于该方法涉及敏感特征的人口比例估算，我们尝试将其扩展到敏感定量变量。此外，为了照顾个人对 DR、RR 和 ICT 的不同选择，并保护受访者选择的隐私，本文开发了一种 ORR 装置，允许通过一般抽样设计选出的受访者根据自己的选择从三个选项中任选一个。国际统计科学杂志》，第 24（1）卷，2024 年 3 月，第 155-170 页

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International Journal of Statistical Sciences

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