Journal of Statistical Planning and Inference 100 (2002) 239–247 www.elsevier.com/locate/jspi Estimation of sensitivity level of personal interview survey questions Sat Gupta ∗ , Bhisham Gupta, Sarjinder Singh Department of Mathematics and Statistics, University of Southern Maine, 96 Falmouth St., PO Box 9300, Portland, Maine 04104-9300 USA Abstract In this paper, an optional randomized response model is proposed. The estimator of the mean of the stigmatized variable based on the optional randomized response sampling is shown to be more ecient than the usual estimator of the mean based on randomized response technique method. In addition to estimating population mean and variance, it has been shown that the optional randomized response technique is useful in quantifying the sensitivity levels of the questions in the personal interview surveys. An estimator for the sensitivity level of a question is proposed and an empirical study is carried out to show the validity of the proposed estimation technique. We also propose a test for the sensitivity level of the stigmatized variable. c  2002 Elsevier Science B.V. All rights reserved. MSC: 62D05 Keywords: Method of moment estimation; Randomized response sampling; Sensitivity of personal interview questions; Estimation of the mean and the variance; Empirical study; Relative eciency 1. Introduction The development of randomized response models for personal interview surveys has attracted a lot of attention after the pioneering work of Warner (1965). Several randomized response models have been developed by researchers for collecting data on both the qualitative and the quantitative variables. For details, one can refer to Tracy and Mangat (1996, 1998), Singh, Horn and Chowdhuri (1998), Singh et al. (1998), Franklin (1989a, 1989b), Mangat and Singh (1990, 1991, 1995), Tracy and Osahan (1995), Mangat et al. (1995a, 1995b, 1995c, 1997), Chaudhuri and Mukerjee (1988), and Greenberg et al. (1969). In addition to theoretical developments, several researchers such as Kerkvliet (1994) have shown applicability of the randomized response models in the real life situations. * Corresponding author. E-mail addresses: sgupta@usm.maine.edu (S. Gupta), bcgupta@usm.maine.edu (B. Gupta), sarjinder@ yahoo.com (S. Singh). 0378-3758/02/$-see front matter c  2002 Elsevier Science B.V. All rights reserved. PII:S0378-3758(01)00137-9