The optimal sample size in the crosswise model for sensitive questions

Stanisław Jaworski ¹   ; Wojciech Zieliński ¹

¹ Department of Econometrics and Statistics Warsaw University of Life Sciences 02-767 Warszawa, Poland

Applicationes Mathematicae, Tome 50 (2023) no. 1, pp. 21-34

Résumé

For interval estimation of the fraction of the population with a stigmatizing characteristic, the nonrandomized response model proposed by Tian, Yu, and Geng (2007) is considered. The most common method for constructing a confidence interval (c.i.) is through the application of the Central Limit Theorem. Unfortunately, such c.i.’s do not maintain the prescribed confidence level, in contradiction to Neyman’s (1934) definition of c.i. In the present paper, the exact c.i. for this fraction is constructed, i.e., the c.i. which keeps the given confidence level. The length of the proposed c.i. depends on the given probability of a positive answer to the neutral question, and on the sample size. For such c.i.’s, the probability of a positive answer to the neutral question is established with respect to the given limit on privacy protection of the interviewee, and the optimal sample size for obtaining the c.i. of a given length is derived.

Détail

DOI : 10.4064/am2486-11-2023

Keywords: interval estimation fraction population stigmatizing characteristic nonrandomized response model proposed tian geng considered common method constructing confidence interval through application central limit theorem unfortunately maintain prescribed confidence level contradiction neyman definition nbsp nbsp present paper exact fraction constructed nbsp which keeps given confidence level length proposed depends given probability positive answer neutral question sample size probability positive answer neutral question established respect given limit privacy protection interviewee optimal sample size obtaining given length derived