General randomized response techniques using Polya's Urn process as a randomization device.

Mashail M Al-Sobhi,Bander Al-Zahrani,Zawar Hussain,Enrique Hernandez-Lemus

doi:10.1371/journal.pone.0115612

Mashail M Al-Sobhi, Bander Al-Zahrani + Show 2 more

Open Access

https://doi.org/10.1371/journal.pone.0115612

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Abstract

In this paper, interesting improvements in [1] and [2] randomized response techniques have been proposed. The proposed randomized response technique applies Polya's urn process (see [3]) to obtain data from respondents. One of the suggested technique requires reporting the number of draws to observe a fixed number of cards of certain type. On the contrary, the number of cards of a certain type is to be reported in case of second proposed randomized response model. Based on the information collected through the suggested techniques, two different unbiased estimators of proportion of a sensitive attribute have been suggested. A detailed comparative simulation study has also been done. The results are also supported by means of a small scale survey.

Highlights

Surveys and questionnaires are usual statistical tools for obtaining data about attitudes, behaviors, emotions, and so forth
C1~c2~0, we have of the estimator p^2 relative to p^Kuk and p^SG
The relative efficiency (RE) results are displayed in S1 Table available in the supporting information files

Summary

Introduction

Surveys and questionnaires are usual statistical tools for obtaining data about attitudes, behaviors, emotions, and so forth. Under the assumptions of randomness of the drawing of balls and truthful reporting of answers, obviously, the total number of yes responses in a sample of n respondents follows a binomial distribution with parameters n and g=(gzr). If a respondent belongs to sensitive group G, he/she is instructed to draw cards, one by one using with replacement, from the first deck of cards until he/she gets the first card bearing the statement of his/her own status, and requested to report the number of cards, say. If a respondent belongs to non-sensitive group G, he/she is instructed to draw cards, one by one using with replacement drawing, from the second deck of cards until he/she gets the first card bearing the statement of his/her own status, and requested to report the number of cards, say Y, drawn by him/her to obtain the first card of his/her own status. We present two new RRTs using Polya’s urn scheme

Proposed RRT I

Proposed RRT II

Discussion and Conclusion