Statistical efficiency of using two quantitative randomized response techniques to estimate correlation.

Abstract

techniques were used to generate sampling distributions of the correlation coefficient between two variables, each measured by two quantitative models of the randomized response technique (RRT): The additive constants model and the unrelated question model. Various parameter combinations were explored and the resulting standard errors for the RRT models and direct questioning are reported. As expected, the RRT models yield less statistically efficient estimates of the population correlation coefficient, and inefficiency increases as the population correlation increases. Comparisons of efficiency between the two models favor the additive constants model for constants less than certain limiting values. Warner's (1965) randomized response technique (RRT) was designed to eliminate evasiveness in response to questions of a sensitive, possibly embarrassing or stigmatizing nature that require a dichotomous response. In Warner's technique, the respondent is presented with two questions, the sensitive question (e.g., Have you ever had an abortion?) and its logical complement (e.g., Have you never had an abortion?). With the aid of a randomizing device, the respondent is directed to answer the sensitive question with probability P and to answer its logical complement with probability 1 -P. Because only the respondent knows to which question the answer pertains, the technique provides confidentiality and should increase the respondent's willingness to truthfully answer sensitive questions.Warner (1965) showed that estimates of population parameters could be derived by applying elementary probability theory. Because of the added randomization process, however, Warner's technique was quite inefficient statistically. Since then considerable efforts have been made to develop other RRT models with greater efficiency (see reviews by Fox & Tracy, 1980;Horvitz, Greenberg, & Abernathy, 1976).In addition to RRT models for categorical questions, a number of models have been developed for questions that require a quantitative or numerical response (e.g., How many abortions have you had? What is your income?). In the quantitative version of the unrelated question RRT (Greenberg, Abul-Ela, Simmons, & Horvitz, 1969), the respondent is directed by the randomizing device to give a numerical response to the sensitive question with probability P and to give a numerical response to a totally unrelated and innocuous question with probability 1 -P. Another RRT model that can be applied to quantitative responses is the linear RRT (Himmelfarb & Edgell, 1980;Pollock

The Multi-Item Randomized Response Technique

“…That is not the case, as has been demonstrated in articles on RRT-based correlation coefficients (e.g., Edgell, Himmelfarb, and Cira 1986;J. A.…”

“…The emphasis in the RRT literature on developing more efficient models, while essential, unfortunately has led to an erroneous but common set of beliefs among applied researchers that the RRT yields only group estimates of population parameters, that scores for individuals cannot be obtained, and that the relationship between a variable measured by the RRT and other variables cannot be assessed on an individual basis. That is not the case, as has been demonstrated in articles on RRT-based correlation coefficients (e.g., Edgell, Himmelfarb, and Cira 1986;J. A.…”

Improving the Measurement of Criminal Sexual Behavior

“…It is also necessary to set an optimal probability of answering the sensitive questiona probability that maximizes the perception of anonymity and minimizes the standard error of the estimate. Research indicates that this value is at least .7 (Carr, Marascuilo, & Busk, 1982;Edgell, Himmelfarb, & Cira, 1986;Fox & Tracy, 1984).…”

A Survey Design for a Sensitive Binary Variable Correlated with Another Nonsensitive Binary Variable

“…. , 4 ) is adopted as the prior distribution of , then the completedata posterior distribution is a grouped Dirichlet (GD) distribution with the formal definition given by (A.2); that is,…”

“…Fox and Tracy [3] derived estimation of the Pearson product moment correlation coefficient between two sensitive questions by assuming that randomized response observations can be treated as individual-level scores that are contaminated by random measurement error. Edgell et al [4] considered the correlation between two sensitive questions using the unrelated question design or the additive constants design. Christofides [5] presented a randomized response technique with two randomization devices to estimate the proportion of individuals having two sensitive characteristics at the same time.…”