RANDOMIZED RESPONSE DESIGNS CONSIDERING THE PROBABILITY OF DISHONEST ANSWERS

When using the randomized response technique to estimate a proportion π associated with some kind of stigmatizing characteristic in a population, researchers have always made the assumption that a respondent will respond truthfully or honestly to statements concerning his or her membership of the stigmatized group. In this paper, we propose a design which eliminates the necessity of this assumption examining first the original design of Warner (1965) to obtain an estimator after removing this assumption and instead include an estimate of the probability of dishonest answers. Using a model which specifies the probability of a dishonest answer, our proposed estimator for π is obtained. The optimal choice of sampling design parameters is discussed and robustness with respect to the optimal parameter values is also investigated. A sampling procedure applicable to practical situations is recommended. The variance of this estimator is compared numerically with that of the corresponding Warner's estimator without the honesty assumption, based on the results, an analysis of estimators with reduced variances is carried out. Finally, a two-trial related question randomized response estimator with variances lower in most cases than those of the corresponding Warner's estimator and the estimator proposed earlier is examined.