Testing the Mixing Property of the Newcomb-Benford Profile: Implications for the Audit Context

  •  Edward Lusk    
  •  Michael Halperin    


Introduction: Circa 1996 Theodore Hill offered a definitive proof that under certain conditions a data generating process is likely to produce observations that follow the Newcomb-Benford Log10 (N-B) first digit profile. The central feature of Hill’s proof is the mixing property from which seems to follow base invariance for scale transformations. Further, it has been observed that small datasets are often not part of the N-B profile set. Study Precise: This suggests that, if indeed the mixing process underlies the generation of the N-B profile, that one should be able to take small Non-Conforming base-invariant datasets that are generated by uncorrupted processes and aggregate them to form datasets that conform to the N-B profile. Results: We demonstrate mixing convergence and find a systematic movement from Non-Conformity to Conformity at a transition point on the order of 250 data points. Impact: We suggest the practical importance of the Hill-Mixing result for the certification audit. We have all of these tests, datasets and results coded in a Decision Support System in VBA: ExcelÔ that is available from the authors free without restriction to its use.

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