“Scrambling” geo-referenced data to protect privacy induces bias in distance estimation

Abstract

Privacy concerns regarding the sharing of spatially referenced household data have induced researchers and survey agencies to “scramble” geographic information by adding random spatial errors to true location coordinates. In this paper, we prove mathematically that the addition of random noise leads to a systematic overestimation of distances between households and access points of interest. We illustrate this average distance bias as well as the attenuation bias generated by random spatial errors using data on household and health facility location from a Health and Demographic Surveillance Site in rural South Africa. Given the large overall biases observed, we argue that the use of scrambled spatial data for policy making or empirical work is generally not advisable, and that alternative methods of protecting data confidentiality should be used to ensure the usability of spatial data for quantitative analysis.