Benford's Law as an instrument for fraud detection in surveys using the data of the Socio-Economic Panel (SOEP)

This paper focuses on fraud detection in surveys using Socio-Economic Panel (SOEP) data as an example for testing newly methods proposed here. A statistical theorem referred to as Benford's Law states that in many sets of numerical data, the significant digits are not uniformly distributed, as one might expect, but rather adhere to a certain logarithmic probability function. To detect fraud we derive several requirements that should, according to this law, be fulfilled in the case of survey data. We show that in several SOEP subsamples, Benford's Law holds for the available continuous data. For this analysis, we have developed a measure that reflects the plausibility of the digit distribution in interviewer clusters. We are able to demonstrate that several interviews that were known to have been fabricated and therefore deleted in the original user data set can be detected using this method. Furthermore, in one subsample, we use this method to identify a case of an interviewer falsifying ten interviews who had not been detected previously by the fieldwork organization. In the last section of our paper, we try to explain the deviation from Benford's distribution empirically, and show that several factors can influence the test statistic used. To avoid misinterpretations and false conclusions, it is important to take these factors into account when Benford's Law is applied to survey data.