On Reproducibility of Statistical Test Based on Randomised Response Data

On reproducibility of hypothesis tests based on randomised response data
Fatimah Alghamdi, Frank Coolen, Tahani Coolen-Maturi
University of Durham

Randomised response techniques (RRT) are frequently used when data on possibly sensitive information is being collected by using a survey. There are many different RRT methods and strategies which seek to know the truth from the respondents with more efficiency and more privacy and without embarrassment besides its ability to decrease the bias which can happen by wrong answers; the first techniques were presented by Warner (1965), then Greenberg model (1979) who has modified some properties in Warner. A question of interest in hypothesis test scenarios is the reproducibility of the results: if the test is repeated, would it lead to the same conclusion concerning the rejection of the null hypothesis? We address this question for Greenberg's method. We use nonparametric predictive inference, a frequentist approach based on only a few assumptions, to derive lower and upper probabilities for test reproducibility. This poses the challenging question of finding another measurement, which is called the measurement of the lower reproducibility probability (MRP), to compare between the Warner and Greenberg test. Greenberg model is more efficient than the Warner model and the measurement MRP and the area of non-rejection of the measurement (AUMRP) of Greenberg test are higher as well. The work will continue to explore more useful results and real applications about (RRT) and it can be developed in another direction.

Reference
[1] Warner, S. L. (1965). Randomized response: A survey technique for eliminating evasive answer bias. Journal of the American Statistical Association 60(309), 63–69. [2] Greenberg, B. G., Abul-Ela, A. L. A., Simmons, W. R., Horvitz, D. G. (1969). The unrelated question randomized response model: Theoretical framework. Journal of the American Statistical Association, 64(326), 520-539.

- Fatimah M. Alghamdi Princess Norah bint Abdulraham University, Saudi Arabia, Fmalghamdi@pnu.edu.sa
- Frank P. A. Coolen Durham University, UK frank.coolen@durham.ac.uk
- Tahani Coolen-Maturi Durham University, UK tahani.maturi@durham.ac.uk