Variance jackknife estimation for randomized response surveys: A simulation study and an application to explore cheating in exams and bullying

Abstract

The aim of the randomized response (RR) technique is to decrease social desirability bias, thus guaranteeing confidentiality, improving respondent cooperation, and obtaining reliable estimates. This technique obtains stronger estimates of sensitive characteristics, compared to direct questioning, by reducing respondents motivation to report falsely their attitudes. In this paper, we have considered the problem of estimation of variance of an estimator based on an RR survey data obtained from a complex survey design by using resampling techniques. The performance of the proposed jackknife modified estimator is tested by simulation studies. The simulation studies reveal that there is a decrease in the relative bias and the relative mean square error for all RR schemes. An RR survey was conducted to investigate sensitive behaviors such as cheating in exams and bullying. The application of the new jackknife confidence intervals revealed substantial increase in high‐tech cheating and bullying in the university campuses.

Regression Models in Complex Survey Sampling for Sensitive Quantitative Variables

“…The jackknife estimation of variance of an estimator of the population mean based on a RR survey data is considered in [43,44]. The authors show that the jackknife estimator underestimates the variance of the Horvitz-Thompson estimator of the population mean and propose modifications of the conventional jackknife estimator.…”