Reproducibility of Statistical Inference Based on Randomised Response Data

Reproducibility of an experiment’s conclusion is an important topic in a variety of fields, including social studies. This thesis presents a theory of reproducibility of statistical inference based on randomised response data. First, reproducibility of statistical hypothesis tests based on randomised response data is studied. This thesis presents statistical inference for reproducibility of the outcome of a hypothesis test based on data resulting from different randomised response techniques (RRT). Secondly, a new method for quantifying reproducibility of statistical estimates is introduced. Finally, this method is applied to derive reproducibility of estimates of population characteristics based on randomised response data. The quantification of reproducibility uses nonparametric predictive inference (NPI), which is suitable for reproducibility when considering this as a prediction problem. NPI uses only few model assumptions and results in lower and upper reproducibility probabilities. We compared different randomised response methods. The results of this thesis open up the possibility of pre-selecting a randomised response method with higher reproducibility and also indicate the relationship between variance and reproducibility with the same privacy level. We find that less variability in the reported responses of RRT methods leads to higher reproducibility of statistical hypothesis tests based on RRT data with the same privacy degree. Therefore, for RRT methods using binary responses, reproducibility of hypothesis tests based on the forced method is greater than reproducibility of hypothesis tests based on the Greenberg method. For RRT methods using real-valued responses, reproducibility of estimates is greater for data collected from the Greenberg method than the reproducibility of estimates for data collected from the optional multiplicative method and the Eichhorn and Hayre method.