National COVID numbers — Benford’s law looks for errors

Australian National University, Canberra, Australia.

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Swiss Federal Institute of Technology, Zurich, Switzerland.

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Given the importance of accurate reporting of COVID-19 cases and deaths to strategies for virus control, we screened countries’ daily records for possible misreporting by applying Benford’s law. This can pick up unreliable numbers resulting from error, oversight or manipulation, for instance — although it cannot distinguish their possible causes.

Benford’s law predicts the relative frequency distribution of first digits in real-world number sets (see M. Sambridge et al. Geophys. Res. Lett. 37, L22301, 2010). Anomalies have exposed financial fraud, for example (see M. J. Nigrini J. Am. Tax. Assoc. 18, 72–91; 1996). We tested data reported by 51 countries from 16 January until 9 April 2020, when case numbers were still on the rise. Once these start to level out, as was the case for China and South Korea over that period, Benford’s law can no longer be applied.

We found that records of cumulative infections and deaths from the United States, Japan, Indonesia and most European nations adhered well to the law (see and therefore are consistent with accurate reporting. Figures from a few of the countries analysed reveal anomalies. These could be explained by limited data sets or by adjustments to avoid headline-grabbing numbers of deaths in the hundreds or thousands.

Nature 581, 384 (2020)

doi: 10.1038/d41586-020-01565-5

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