Improved randomized response models using three decks of cards

Abstract

Odumade and Singh [10] have extended the Warner randomized response model [15] by the use of two decks of cards. In this paper, a new randomized response model based on the use of three decks of cards is proposed as an extension to the Odumade and Singh model [10]. The Cramer-Rao lower bound of the variance of the proposed estimator has been obtained. An empirical study has also been performed to compare the lower bound of the variance of the new estimator with that developed by Singh and Sedory [14]. The new estimator turned out to be more efficient than the Singh and Sedory estimator [14] but the problem of low level of respondents' cooperation can be accompanied with the new model. In an attempt to maintain the respondents' privacy and thereby increase the level of their cooperation, another model using three decks of cards was suggested. When comparing the two proposed models, it was found that the second model can be easily adjusted to be more efficient than the first model; moreover it can largely increase the respondents' cooperation as there is a chance that the respondent will answer the sensitive question only once or twice.