Bootstrap Approach to the Application of First‐Digits Analysis

Matthew Corrigan and Emily Roche

Abstract

The distribution of first-digits obtained from many natural and economic datasets seem to follow a consistent distribution. The desire to find anomalies such as detecting fraud in financial and scientific datasets are common, and applications of "Benford's Law" have been developed to find these anomalies. In our work with applying these methods to determine interviewer anomalies we found that interviewer's assigned caseloads contained data where stratified subsets of first-digits follow consistent distributions that are like Benford's, but not specifically Benford's. To observe an interviewer objectively, we created a profile distribution by subsampling a mixture from available distributions to match individual interviewer's profile distribution. Using the interviewer's proportion of first-digits as a test statistic, we are able to determine bootstrapped p-values for first-digits in a way that allows us to flag interviewer results as suspicious and in need of closer scrutiny.