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

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