On the Sample Size Determination based on the Randomized Response Surveys

Abstract

In general, the well known Chebyshev’s inequality is used to determine the sample size in order to conduct a survey using direct responses. The same technique intending to cover for sensitive variables are attempted recently by many statisticians. However it has been observed that in many cases the acceptable sample sizes are hard to be obtained, mainly because of appearance of some easily non-controllable part. Chaudhuri and Sen (2020), Chaudhuri and Patra (2023) and others have illustrated different situations and solutions are proposed therein. In this paper, following Chaudhuri, Bose and Dihidar (2011), we have made an attempt to deterimine the sample size corresponding to the estimators of sensitive population proportion using multiple randomized responses from distinct persons sampled. Along with the theoretical derivations, some numerical illustrations are presented. Based on the important extractions of our numerical illustration results, the recommendable sample size in practical real survey situations are observed.

International Journal of Statistical Sciences, Vol. 24(1) March, 2024, pp 115-132