Affiliations: School of Studies in Statistics, Vikram University, Ujjain, India
Corresponding author: Housila P. Singh, School of Studies in Statistics, Vikram University, Ujjain 456010, India. E-mail: [email protected].
Abstract: This paper addresses the problem of estimating the population proportion πS possessing the sensitive attribute using stratified random sampling. Two alternatives to Kim and Warde  stratified randomized response model have been proposed. The proposed models are based on extending Singh  models to the case of stratified random sampling. It has been shown that the proposed models are more efficient than Kim and Warde  stratified randomized response technique under some realistic conditions in both the cases of completely truthful reporting and that of not completely truthful reporting by the respondents. A practical problem with the use of optimum (Neyman) allocation has been pointed out. Thus, in practice, the use of either proportional allocation or equal allocation has been suggested while estimating proportion of a sensitive attribute using stratified randomized response sampling. Numerical illustrations and graphs are also given in support of the present study.
Keywords: Randomized response technique, stratified random sampling, dichotomous population, sensitive attribute, estimation of proportion, bias, mean square error