International Journal of Business and Social Science Vol. 1 No. 1; October 2010 186 A New Mixed Randomized Response Model Ayesha Nazuk NUST Business School Islamabad, Pakstan E-mail: Ayesha.nazuk@nbs.edu.pk Phone: 0092-51-9085-3267 Javid Shabbir Department of Statistics Quaid-i-Azam University Islamabad, Pakistan Abstract In this study we present a modification of Kim and Warde (2004) model to estimate the proportion of a qualitative sensitive variable. It has been numerically shown that the proposed model performs better than the model of Kim and Warde (2004) and Moors (1971). Keywords: Randomized response technique (RRT), simple random sampling with replacement, sensitive variable, and innocuous variable. 1.1 Introduction Sensitive study variables are often dealt in survey research such as proportion of adulterated milk packs of a company, proportion of illicit drugs usage, etc. Warner (1965) introduced a technique to estimate the true proportion of qualitative sensitive variable. Greenberg et al. (1971) presented a revised version of Warner (1965) technique for qualitative variables. As far as qualitative sensitive variables are concerned, many researchers have modified the Warner (1965) model, some of them include Mangat et al. (1997), Singh et al. (2000), Chang and Huang (2001), Chang et al. (2004), and Gupta et al. (2006). Kim and Warde (2004) presented a new randomized response model using simple random sample with replacement sampling scheme which improves the privacy of respondents. In this paper we have modified the Kim and Warde (2004) model to estimate the proportion of qualitative sensitive variable. Main aim of modification has been to reduce the variance of estimator, for proportion of qualitative sensitive variable, and to improve the privacy protection of the respondents. 2.1 Proposed Model Let a random sample of size n be selected using simple random sampling with replacement. Each respondent in the sample is instructed to answer an innocuous question “I possess the innocuous characteristic Y ”. If the answer to the initial direct question is “Yes” then the respondent is instructed to go to randomization device 1 R . otherwise to 2 R. Where 1 R consists of two statements (i) “I belong to sensitive group” and (ii) “I belong to the innocuous group”, with respective probability 1 p and 1 (1 ) p - . While 2 R consists of the same pair of statements as in 1 R but with respective probability 2 p and 2 (1 ) p - . In order to offer privacy to the respondents they are not required to tell that which randomizing device they have used. Let 1 n and 2 n be the number of respondents using 1 R and 2 R respectively such that ( ) 1 2 n n n + = .