Scrambled randomized response methods for obtaining sensitive quantitative data

An Improved Bar Lev, Bobovitch and Boukai Randomized Response Model Using Moments Ratios of Scrambling Variable

“…Later on, with known coefficient of variation C Y of the study variable Y various authors including Khan (1967), Govindarajulu and Sahai (1972), Gleser and Healy (1976), Sen (1979), In this paper we have suggested a new randomized response model and its properties are studied. It has been shown that the resulting (optimum) randomized response model depends on the moments ratios such as C γ (coefficient of variation), β 1(S) (coefficient of skewness) and β 2(S) (coefficient of kurtosis) of the scrambling variable S. We have proved the superiority of the proposed randomized response model over Eichhorn and Hayre (1983) and Bar Lev et al (2004) randomized response models both theoretically and empirically.…”

“…For more examples, the reader is referred to Ahsanullah and Eichhorn (1988). According to Eichhorn and Hayre (1983), each respondent in the sample is requested to report the scrambled response Z i = SY i , where Y i is the real value of the sensitive quantitative variable, and S is the scrambling variable whose distribution is assumed to be known. In other words E(S) = θ andV (S) = γ 2 are assumed to be known and positive, where E and V denote the expected value and variance over the randomization device.…”

“…In other words E(S) = θ andV (S) = γ 2 are assumed to be known and positive, where E and V denote the expected value and variance over the randomization device. Then an estimator of the population mean µ y under the simple random sampling with replacement (SRSWR) due to Eichhorn and Hayre (1983) is given by:…”

E-research – selected issues concerning the Internet attitudes and opinions research

“…Scholars have assessed the method's efficiency within various designs (e.g., Moors 1971;Dowling and Shachtman 1975;Pollock and Bek 1976) and compared them to estimates from direct questioning (e.g., Lensvelt-Mulders, Hox, and Van Der Heijden 2005a;Krumpal 2012;Gingerich et al 2014;Rosenfeld, Imai, and Shapiro 2015). The design originally outlined by Warner (1965) has been extended to incorporate multiple sensitive traits (Abul-Ela, Greenberg, and Horvitz 1967;Christofides 2005), multiple sensitive questions (Raghavarao and Federer 1979;Tamhane 1981), responses on a Likert scale (Himmelfarb 2008;De Jong, Pieters, and Fox 2010), and quantitative answers (Eichhorn and Hayre 1983;Fox and Tracy 1984). Recent work has explored flexibility in sampling procedures (Chaudhuri 2001;Chaudhuri and Saha 2005;Chaudhuri 2011).…”

A new estimator based on auxiliary information through quantitative randomized response techniques

“…Thornton and Gupta (2004) extended Warner's (1971) approach by using partial additive models for estimating the mean of sensitive quantitative variables in RRT. The multiplicative model was later investigated in depth by Eichhorn and Hayre (1983), who referred to it as the scrambled responses method. Similarly, Bar-Lev, Bobovitch, and Boukai (2004) proposed a method which uses a partial model that generalizes Eichhorn and Hayre's results and yields an estimate which, under mild conditions, has a uniformly smaller variance.…”