Reproducibility of Statistical
Inference Based on Randomised
Response Data

Abstract

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.