Detecting Newcomb-Benford Digital Frequency Anomalies in the Audit Context: Suggested Chi2 Test Possibilities

Lusk, Edward J.; Halperin, Michael

doi:10.5430/afr.v3n2p191

Cited by 6 publications

(6 citation statements)

References 9 publications

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“…In this regard, Lusk & Halperin (2014b) argue that if the overall computed is > 15.507 which is the 95% inferential cut-off, that the dataset is Non-Conforming in nature. Also in this regard, the sample size anomaly does not come into play as the sample sizes were projected using the upper limit suggested by Lusk & Halperin (2104b) of 440.…”

Section: Robustness Testing Of the Principal Bpp Resultsmentioning

confidence: 99%

“…"Listing" is a critical accrual criterion as this suggests that there was no evidence that the data generating processes of the firm were inappropriately modified, corrupted, or constrained so as not to be representative of generating processes that would be expected to produce data that would conform to the Newcomb-Benford profile. Here the research of Ley (1996); Nigrini and Mittermaier (1997); Durtschi, Hillison and Pacini (2004); Reddy and Sabastin (2012) and Lusk and Halperin (2014b) taken together suggest that Corrupted data generating processes often do not produce data that follows…”

Section: The Datasets Used To Test the Mixing Transitionmentioning

confidence: 96%

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

Lusk¹,

Halperin²

2014

IJEF

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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: Excel™ that is available from the authors free without restriction to its use.

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Section: Robustness Testing Of the Principal Bpp Resultsmentioning

confidence: 99%

Section: The Datasets Used To Test the Mixing Transitionmentioning

confidence: 96%

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

Lusk¹,

Halperin²

2014

IJEF

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“…What still governs is the overall chi-square; this is the only statistically-based inference signal that can be used. Finally, it is also the case that direct benchmarking creates a risk for the FP error anomaly as illustrated by Lusk and Halperin (2014b;2014c) where they argue for two random samples with sample size control in the range [315 to 440]. This then rationalizes the various cell profiles that we will now use in our ARL profiling.…”

Section: Profiling Screening Recommendationsmentioning

confidence: 89%

“…The BPP was derived using Benford's 20 datasets that were realizations from many different experiential-i.e., real "contexts" -and so embodies the natural variation that may aid the SCB analyst in focusing on practical differences in comparative profiles, and 2. Using the Benford datasets an interval screening test, see Table 1 (BSW: Cols 3 & 4), developed by Lusk and Halperin (2014a;2014b;2014c) will greatly facilitate profile differentiation.…”

Section: A Practical Extension Of the Log 10 Profilementioning

confidence: 99%

Navigating the Benford Labyrinth: A big-data analytic protocol illustrated using the academic library context

Halperin¹,

Lusk

2016

Knowledge Management &Amp; E-Learning: An International Journal

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Objective: Big Data Analytics is a panoply of techniques the principal intention of which is to ferret out dimensions or factors from certain data streamed or available over the WWW. We offer a subset or “second” stage protocol of Big Data Analytics (BDA) that uses these dimensional datasets as benchmarks for profiling related data. We call this Specific Context Benchmarking (SCB). Method: In effecting this benchmarking objective, we have elected to use a Digital Frequency Profiling (DFP) technique based upon the work of Newcomb and Benford, who have developed a profiling benchmark based upon the Log10 function. We illustrate the various stages of the SCB protocol using the data produced by the Academic Research Libraries to enhance insights regarding the details of the operational benchmarking context and so offer generalizations needed to encourage adoption of SCB across other functional domains. Results: An illustration of the SCB protocol is offered using the recently developed Benford Practical Profile as the Conformity Benchmarking Measure. ShareWare: We have developed a Decision Support System called: SpecificContextAnalytics (SCA:DSS) to create the various information sets presented in this paper. The SCA:DSS, programmed in Excel VBA, is available from the corresponding author as a free download without restriction to its use. Conclusions: We note that SCB effected using the DFPs is an enhancement not a replacement for the usual statistical and analytic techniques and fits very well in the BDA milieu.

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“…Therefore, our testing result here can be used to verify the acuity of the NBDSSP in relation to the FNSE, especially as we narrow down the sample sizes to the range of 250 to 440 which are the range intervals for the low-end test by BLHL and the high-end tested by Lusk and Halperin (2014b). If the Hill dataset were to have been scored as Confirming at a high frequency for smaller sample sizes then this would call into question the acuity of the NBDSSP relative to the FNSE.…”

Section: The False Negative Signaling Error: Incorrectly Believing Thmentioning

confidence: 99%

Full Range Testing of the Small Size Effect Bias for Benford Screening: A Note

Bao¹,

Heilig²,

Lee³

et al. 2018

IJEF

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Bao, Lee, Heilig, and Lusk (2018) have documented and illustrated the Small Sample Size bias in Benford Screening of datasets for Non-Conformity. However, their sampling plan tested only a few random sample-bundles from a core set of data that were clearly Conforming to the Benford first digit profile. We extended their study using the same core datasets and DSS, called the Newcomb Benford Decision Support Systems Profiler [NBDSSP], to create an expanded set of random samples from their core sample. Specifically, we took repeated random samples in blocks of 10 down to 5% from their core-set of data in increments of 5% and finished with a random sample of 1%, 0.5% & 20 thus creating 221 sample-bundles. This arm focuses on the False Positive Signaling Error [FPSE]-i.e., believing that the sampled dataset is Non-Conforming when it, in fact, comes from a Conforming set of data. The second arm used the Hill Lottery dataset, argued and tested as Non-Conforming; we will use the same iteration model noted above to create a test of the False Negative Signaling Error [FNSE]-i.e., if for the sampled datasets the NBDSSP fails to detect Non-Conformity-to wit believing incorrectly that the dataset is Conforming. We find that there is a dramatic point in the sliding sampling scale at about 120 sampled points where the FPSE first appears-i.e., where the state of nature: Conforming incorrectly is flagged as Non-Conforming. Further, we find it is very unlikely that the FNSE manifests itself for the Hill dataset. This demonstrated clearly that small datasets are indeed likely to create the FPSE, and there should be little concern that Hill-type of datasets will not be indicated as Non-Conforming. We offer a discussion of these results with implications for audits in the Big-Data context where the audit In-charge may find it necessary to partition the datasets of the client.

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Detecting Newcomb-Benford Digital Frequency Anomalies in the Audit Context: Suggested Chi2 Test Possibilities

Cited by 6 publications

References 9 publications

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

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

Navigating the Benford Labyrinth: A big-data analytic protocol illustrated using the academic library context

Full Range Testing of the Small Size Effect Bias for Benford Screening: A Note

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