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This poster won the 2019 Harvard University Postdoctoral Symposium. The poster shows how to use differential privacy with negligible utility loss to facilitate the replication and reuse of statistical analysis of sensitive datasets. We illustrate our approach with the case of the Internet Connectivity Statistics, a high-precision statistical dataset estimated from BGP traffic, that has potential privacy and ethical implications. We apply a differential privacy algorithm to compute privacy-preserving statistics, and we compare them with the original method. Our statistical test shows that the privacy-preserving estimates match the accuracyof the original method up to the 5th decimal of the Pearson correlation coefficients, therefore offering a negligible utility loss. We also show how the resulting statistics can be safely shared for reuse and replication deploying a Dataverse and a simplified version of the Datatags system. Our approach contributes to the field by 1) showing how to apply differential privacy algorithms for Political Science research; 2) making available the most precise Internet connectivity data available; 3) enabling other researchers to use our data compliant with reproducibility standards, Open Science and the FAIR principles. Co-authors: James Honaker and Merce Crosas, Harvard University.