On some new randomized item sum techniques

A recent quantified version of item count technique (ICT), called the item sum technique (IST), was developed by Trappmann et al. (2014 Trappmann, M., I. Krumpal, A. Kirchner, and B. Jann. 2014. Item sum—A new technique for asking quantitative sensitive questions. Journal of Survey Statistics and Methodology 2 (1):58–77. doi:10.1093/jssam/smt019.Crossref] , Google Scholar]). In this method, two subsamples are required to obtain reliable data on the sensitive issues. In this article, we propose three alternative item sum techniques by utilizing an additional randomization device. The main advantage associated with the current study is that in order to estimate population sensitive parameters, it requires only one sample to obtain reliable data on quantitative sensitive issue without jeopardizing the privacy of participants. Furthermore, it reduces the cost, effort, and time as compared to usual IST. It is also free from the requirement of finding optimum subsample sizes as in the usual IST. The mean and variance of these proposed estimators are also derived and compared with those of the usual IST. Through algebraic and nnumerical comparsions, it is observed that the proposed techniques perform better than the usual IST. Moreover, the proposed randomized IST 3 is observed to be unconditionally more effeicient than the proposed IST 1 and IST 2.