Christofides’ randomized response technique in complex sample surveys

Abstract.

Christofides (2003) has given an improved modification of Warner’s (1965) pioneering randomized response (RR) technique in estimating an unknown proportion of people bearing a sensitive characteristic in a given community. As both these RR devices are shown to yield unbiased estimators based only on simple random sampling (SRS) with replacement (WR) but in practice samples are mostly taken with unequal selection probabilities without replacement (WOR), here we present methods of estimation when Christofides’ RR data are available from unequal probability samples. Warner’s (1965) RR device was earlier shown by Chaudhuri (2001) to be applicable in complex surveys. For completeness we present estimators for the variance of our estimator and also describe what to do if some people opt to divulge truths.