Randomized Response Techniques For Complex Survey Designs

Survey questions of a sensitive nature are likely to lead to refusals or untruthful answers. The randomized response(RR) technique to procure trustworthy data on sensitive matters by protecting privacy of the respondents was first introduced by Warner(1965). His model uses two randomized questions both enquiring about the respondent's status in relation to the sensitive character. Over the past few decades, a number of modifications of Warner's method as well as several other new methods have been emerged in the literature of RR.In order to make the repondents more co-operative, Horvitz et al(1967) suggested that one question should enquire about the sensitive characteristic while other should be completely neutral. Then, Moors(1971) improved the Horvitz's model . In 2000, Singh et al proposed two modifications of Moors's model, which do not jeopardize the privacy of respondent.However, most of the RR procedures available in the literature are developed and studied with the restriction that the sample is selected by simple random sampling with replacement. Jong-Min Kim,William D.Warde (2004) proposed a stratified randomized response model based on Warner's(1965).In this paper, the Singh et al's methods are extended to the stratified sampling and unequal probability sampling. Expressions for the unbiased estimator of the population mean and variance have been obtained. Other related properties are also discussed in the paper.