An improved stratified randomized response model using two decks of cards

Abstract

Randomized response technique is an effective research method that is used to estimate the proportion of a population that possesses a sensitive characteristic, such as tax evasion, abortion, or drug abuse. In this paper, two recently developed randomized response models using two decks of cards are extended to the case of stratified random sampling. Under proportional allocation or optimal allocation for fixed sample sizes, it is shown that the proposed stratified estimators are always more efficient than their counterparts in simple random sampling. Comparing the two proposed models, it is found that one of the models can be adjusted to be more efficient than the other, and that this model can increase the respondents' cooperation. Hence this model is referred to as the improved model. For unknown strata sizes, the double sampling method for stratification is applied.