Investigating and preventing scientific misconduct using Benford's Law.

Integrity and trust in that integrity are fundamental to academic research. However, procedures for monitoring the trustworthiness of research, and for investigating cases where concern about possible data fraud have been raised are not well established. Here we suggest a practical approach for the investigation of work suspected of fraudulent data manipulation using Benford's Law. This should be of value to both individual peer-reviewers and academic institutions and journals. In this, we draw inspiration from well-established practices of financial auditing. We provide synthesis of the literature on tests of adherence to Benford's Law, culminating in advice of a single initial test for digits in each position of numerical strings within a dataset. We also recommend further tests which may prove useful in the event that specific hypotheses regarding the nature of data manipulation can be justified. Importantly, our advice differs from the most common current implementations of tests of Benford's Law. Furthermore, we apply the approach to previously-published data, highlighting the efficacy of these tests in detecting known irregularities. Finally, we discuss the results of these tests, with reference to their strengths and limitations.