Improvement upon Warner's model with an optional randomized response technique

Abstract

In sample surveys, it is often difficult to obtain true responses when respondents are asked questions of highly personal or controversial nature. In order to solve this problem, Warner [10] introduced a randomized response technique (RRT), which was developed subsequently by different authors. A summarization of different such techniques can be seen in Fox and Tracy [4], Chaudhuri and Mukerjee [3].

To implement the privacy problem with the quantitative character Mangat and Singh [6], Singh and Joarder [9], Gupta et al. [5], Arnab [1] and Pal [7] discussed an Optional Randomized Response (ORR) technique to allow an option to a respondent either to give out a Direct Response (DR) or a randomized response (RR) following a prescribed device without divulging their actual options. This approach discussed here tries to extend this technique to cover qualitative forms of sensitive variables for complex survey designs. Theoretical comparison of ORR and RR models is given here with the restriction of the RR parameters. An unbiased estimator of the proportion of people bearing a sensitive characteristic along with the unbiased variance estimator is also presented here.