Benford's Law Research Articles

Use of Benford's law on academic publishing networks

Benford's law, also known as the first-digit law, has been widely used to test for anomalies in various data ranging from accounting fraud detection, stock prices, and house prices to electricity bills, population numbers, and death rates. Scientific collaboration graphs have been studied extensively as data availability increased. Most research was oriented towards analysing patterns and typologies of citation graphs and co-authorship graphs. Most countries group publications into categories in an attempt to objectively measure research output. However, the scientific community is complex and heterogeneous. Additionally, scientific fields may have different publishing cultures, which make creating a unified metric for evaluating research output problematic. In complex systems like these, it is important to regularly observe potential anomalies and examine them more carefully in an attempt to either improve the evaluation model or find potential loopholes and misuses. In this paper, we examine the potential application of Benford's law on the official research database of Slovenia. We provide evidence that metrics such as number of papers per researcher conform to Benford's distribution, while the number of authors per paper does not. Additionally, we observe some anomalies and provide potential reasoning behind them.

Benford's Law and COVID-19 Data

Benford's law states that in many sets of naturally occurring data, the first significant digit of an arbitrarily chosen data point is not equally likely to be 1, ..., 9, as one might expect, but i...

Can we rely on COVID-19 data? An assessment of data from over 200 countries worldwide.

To fight COVID-19, global access to reliable data is vital. Given the rapid acceleration of new cases and the common sense of global urgency, COVID-19 is subject to thorough measurement on a country-by-country basis. The world is witnessing an increasing demand for reliable data and impactful information on the novel disease. Can we trust the data on the COVID-19 spread worldwide? This study aims to assess the reliability of COVID-19 global data as disclosed by local authorities in 202 countries. It is commonly accepted that the frequency distribution of leading digits of COVID-19 data shall comply with Benford's law. In this context, the author collected and statistically assessed 106,274 records of daily infections, deaths, and tests around the world. The analysis of worldwide data suggests good agreement between theory and reported incidents. Approximately 69% of countries worldwide show some deviations from Benford's law. The author found that records of daily infections, deaths, and tests from 28% of countries adhered well to the anticipated frequency of first digits. By contrast, six countries disclosed pandemic data that do not comply with the first-digit law. With over 82 million citizens, Germany publishes the most reliable records on the COVID-19 spread. In contrast, the Islamic Republic of Iran provides by far the most non-compliant data. The author concludes that inconsistencies with Benford's law might be a strong indicator of artificially fabricated data on the spread of SARS-CoV-2 by local authorities. Partially consistent with prior research, the United States, Germany, France, Australia, Japan, and China reveal data that satisfies Benford's law. Unification of reporting procedures and policies globally could improve the quality of data and thus the fight against the deadly virus.

A Benford's law based method for fraud detection using R Library

Benford Law (BL) states that the occurrence of significant digits in many natural and human phenomena data sets are not uniformly scattered, as one could naively expect, but follow a logarithmic-type distribution. Here, we present a method that consists of the use of BL analysis over first and first-two digits, three statistical conformity tests – Z-statistics, Mean Absolute Deviation (MAD) and Chi-square (χ2) as well as the summation test which looks for excessively large numbers, having fraud detection as one of its application. We developed the method for fraud detection in the case of the Brazilian Bolsa Familia welfare program. In this case, we submitted four periods of Brazilian welfare program payments to the method with a dataset of 13,442,529 records. We provide a practical implementation of the method based on open-source R library released on a public repository. Furthermore, code implementation of the algorithm as well as datasets are freely available. Advantages of the algorithm are listed below:• The method was developed based on open source libraries• The technique is simple, rapid and ease of use• Easily applicable to other social welfare program auditing

Benford’s Law Application: Case of Elections in Sri Lanka

Sri Lanka, like many developing countries has been involved in a circle of allegations of election fraud. Usually these claims are pronounced more by losing parties. This study uses Benford’s law, a law of probability distribution of digits, to investigate whether the election fraud claims might have merit. A sample in this study is made of 808 election data. This data comes from the 2010 Presidential election for representatives from three major political parties and from 2010 General Election data. All of the data points were obtained through reliable government sources, two of which are, the Department of Elections website of Sri Lanka, and the National News Paper statistics (2010). The study contrasts the distribution of the first digit of election results against the Benford’s Law benchmark. After obtaining the results, we organize the data and find median, mean, mode and standard deviation. The preliminary results showe that the data does not align with Benford’s law predictions. In other words, it shows that the data does not follow the law where the mean is larger than the median and there is a positive skewness then it likely follows a Benford’s distribution. The distribution of the first digit of actual data for three parties disagrees with Benford's law. This misalignment is more pronounced for the winning party than for the second and third place parties, respectively. We, therefore, look forward to run the data through several critical analyses and observing if there shall be any fraud or manipulation in numbers.

Application of digits based test to analyse presidential election data in Nigeria

ABSTRACT This study examined the application of Benford's Law to analyse the 2015 and 2019 presidential election data in Nigeria. Data obtained from the electoral body were analysed using frequency distribution and Spearman Rank Correlation tests at 0.05 level of significance. Findings revealed that the second digits distributions of the vote counts for the two major political parties, registered voters and total vote counts in both elections do not conform to the distributional pattern predicted by Benford's Law. The study recommends that stakeholders should aim for an electoral reform that allows the use of forensic analysis of electoral data in Nigeria.

BENFORD YASASI İLE FİNANSAL TABLOLARDAKİ HİLE RİSKİNİN BELİRLENMESİ

The aim of this study is research potential fraud risk in financial statements by using some financial and nonfinancial parameters. For detection of fraud risk used conformity of financial statements with Benford's law among different groups of companies. Variables to be met by financial statement liability include sectors, risk groups, size of independent audit firms, independent auditing obligation and independent membership of directory board. To this intent balance sheet and income statements of the companies traded in BIST real sector for the years 2008-2017, taken as data set. Data set were applied Benford analysis for measuring conformity of financial statements with Benford’s law. For analyse difference between groups applied T-Test, ANOVA and TUKEY tests. As a result, investigated significant difference between company groups and variables were found to affect the fraud risk in the financial statements. These results have shown impact of different variables on financial statement as a fraud risk factor. It has expected that these factors are effective in the financial statement fraud. Company owners, professsional accountants, auditors and tax authority can use this method for detecting red flags and selecting audit targets.

Testing of Published Information on Greenhouse Gas Emissions. Conformity Analysis with the Benford’s Law Method

The issue of greenhouse gas emissions and climate change cannot be overlooked from the scope of concern essential to develop the financial audit profession and implicitly the activity of the financial auditor. Within its professional field, the analysis of data quality on these issues requires applying divers analytical review methods, which incorporates unique statistical or mathematical rules. One of these is the analytical review procedure based on testing compliance of data distribution with Benford’s Law. We present a practical case for testing the verisimilitude of data represented by greenhouse gas emissions, based on the Eurostat database. We applied the Benford's Law method for the first four digits, and the results were tested for likelihood by statistical methods such as Chi-square test or the Kolmogorov-Smirnov test. Information on greenhouse gas emissions is the basis for specific environmental policy decisions, which can be considered at the microor macroeconomic level. If this information is affected by subjective influences, then economic decisions or environmental policies will also be affected. Therefore, the objective of this research to test the plausibility of published data on greenhouse gas emissions proves its usefulness in relation with the actions performed by the economic and social players towards a sustainable development of the economy.

Using Benford's law to assess the quality of COVID-19 register data in Brazil.

We employ Newcomb–Benford law (NBL) to evaluate the reliability of COVID-19 figures in Brazil. Using official data from February 25 to September 15, we apply a first digit test for a national aggregate dataset of total cases and cumulative deaths. We find strong evidence that Brazilian reports do not conform to the NBL theoretical expectations. These results are robust to different goodness of fit (chi-square, mean absolute deviation and distortion factor) and data sources (John Hopkins University and Our World in Data). Despite the growing appreciation for evidence-based-policymaking, which requires valid and reliable data, we show that the Brazilian epidemiological surveillance system fails to provide trustful data under the NBL assumption on the COVID-19 epidemic.

Using Benford's Law to Assess Data Integrity in Two Retracted Papers About COVID-19

Background: Two papers about hospitalizations in patients with COVID-19 that were published in the Lancet and the New England Journal of Medicine were retracted soon after being published because the authors were unable to make the data used in the papers available for audit. The possibility that the data were fabricated was raised in the media but no evidence to refute or confirm this speculation has been presented.Methods: We did an analysis of the numeric data in the two papers to assess their conformance with “Benford’s law,” which states that, for a determined set of “natural” numbers, those whose first digit is 1 will appear more frequently (30.1%) than those beginning with other digits, following in order from 2 to 9 (17.6%, 12.5%, 9.7%, 7.9%, 6.7%, 5.8%, 5.1%, and 4.6%, respectively). Conformance with Benford’s law is evidence that data have not been fabricated since it is difficult to “fake” data.Findings: In both retracted papers, there were statistically significant deviations of the numeric data in the papers from Benford’s law.Interpretation: Violation of Benford's law for first digits is not proof of data falsification or fraud. Whether the retracted papers contained fabricated data, data obtained fraudulently, or data that could not be made available for audit will probably never be known.Funding Statement: This research was not funded.Declaration of Interests: Guido Schuepfer, Jacqueline Mauch, and Diana Petitti declare that they have no financial or personal relationships that create a conflict of interest.

Rounding up performance measures in German firms: Earnings cosmetics or earnings management on a larger scale?

AbstractWe use Benford's Law to provide evidence that German firms round up both their net income and earnings per share. We use the introduction of the euro to show that round earnings numbers are likely the result of earnings management. The incentive to round up comes from stakeholders’ left‐digit bias when processing the information in financial statements. Since round numbers are natural benchmarks, stakeholders perceive the performance metrics directly below such thresholds as abnormally lower. However, rounding up is objectionable only if it involves large‐scale earnings management, but not in cases of negligible ‘earnings cosmetics’. Because the difference between the pre‐managed and reported earnings is unobservable, we investigate whether the prevalence of rounding up coincides with specific levels of several earnings characteristics and proxies for audit quality. If the rounding up is cosmetic, then it should occur independently of these characteristics. In contrast, if firms use earnings management on a larger scale, then it might not be possible to simultaneously round up and achieve other objectives of earnings management. Our evidence is in line with substantial earnings management.

Detecting academic fraud using Benford law: The case of Professor James Hunton

We investigate whether Benford's Law can be used to differentiate retracted academic papers that have employed fraudulent/manipulated data from other academic papers that have not been retracted. We use the case of Professor James Hunton who had 37 of his articles retracted because there were grave concerns that they contained mis-stated or fabricated datasets. We construct several Benford conformity measures, based on first significant digits contained in the articles, to determine whether Hunton's retracted papers differ significantly from a control group of non-retracted articles by competing authors. Our results clearly indicate that Hunton's retracted papers significantly deviate from Benford Law, relative to the control group of papers. In additional analysis we also find these results are generalisable to other authors with retracted papers. Our findings suggest that potentially both co-authors and journals could consider implementing a data analytical tool which employs Benford Law to highlight potential ‘red flag’ papers, with a view to decreasing the risk of fraudulent activity and thereby enhancing the credibility of academic papers and journals.

A quick Look at the Registered Cases of Covid-19 Throughout the World

The present work analyzes the registered cases of Covid-19 throughout the world according the data registered at Johns Hopkins University. We selected 15 countries to analyze their data. In alphabetical order the countries are: Argentina, Australia, Brazil, Chile, China, Colombia, Germany, India, Italy, Mexico, Peru, Portugal, Spain, United States and Venezuela. With this information, three different studies were carried out. First, the data was validated using Benford's Law which is based on forensic techniques that allow us to guarantee the integrity of the information. Later, we calculated the value of the basic reproduction number (R0), ie., the number of secondary host infections caused by one primary host infection that helps us to determine if a country has an outbreak of Covid-19. Finally, we show that the best representation for the change in the number of cases in the time is to calculate the mantissa value, ie., the floating number obtained from the logarithm of the data.

Uniform distribution, Benford’s law and scale-invariance

In this paper we first discuss translation invariant measures and probabilities on $${\mathbb {R}}$$ and then use the results to describe a possible approach to the Benford law.

THE USE OF BENFORD’S LAW IN PERFORMANCE AUDIT TO DETECT FRAUD IN THE STATE EXPENDITURETRANSACTIONS ASSISTED BY IDEA SOFTWARE (A Case Study at the Transportation Ministry Work Units)

The aim ofthis study was to determine the use of Benford's Law in Performance Audits todetect fraudin state expenditure transactions assisted by IDEA Software,a case studyat several Work Units of the Ministry of Transportation. The research method used was descriptive qualitative and direct experiment. This researchwas conucted while the researcher wascarruing outperformance auditat three work units of the Ministry of Transportation. The researcher used IDEA Software to analyze the financial transaction data according to Benford's law. Based on the results of the research, the right type of state expenditure to be analyzed using Benford law isgoods expenditure.In addition,Benford’s Law can be used in performance audits to determinestate expenditure transactions that are indicated fraud with the success rate of ranging from 20% to 50%t. Transactions that appear are not in accordance with Benford's law.

The Inverse Gamma Distribution and Benford's Law

According to Benford's Law, many data sets have a bias towards lower leading digits (about 30% are 1's). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing in competitive sports. There are many common distributions that exhibit such bias, i.e. they are almost Benford.
 These include the exponential and the Weibull distributions. Motivated by these examples and the fact that the underlying distribution of factors in protein structure follows an inverse gamma distribution, we determine the closeness of this distribution to a Benford distribution as its parameters change.

How Valid are the Reported Cases of People Infected with Covid-19 in the World?

The goal of this paper is to analyze the registered cases of people who have been infected with Covid-19 registered from throughout the world, using a digital forensic analysis technique that is based on Benford's Law. Twenty-three countries were randomly chosen for this analysis: China, India, Germany, Brazil, Venezuela, Netherlands, Italy, Colombia, Russia, Norway, South Africa, Portugal, Singapore, United Kingdom, Chile, Ecuador, Egypt, Denmark, Ireland, France, Belgium, Australia and Croatia.. We calculate on the p-values based on Pearson χ2 and Mantissa Arc Test according to the results obtained with the first digit. If any country fails these two tests, a third proof will be carried out based on the Freedman-Watson test. The results indicated that results from Italy, Portugal, Netherlands, United Kingdom, Denmark, Belgium and Chile are suspicions of data manipulation because the numbers fail the Benford’s Law according to the results obtained until April 30, 2020. However, it is necessary to carry out further studies in these countries in order to ensure that they countries manipulate or altered the information.

PENGGUNAAN BENFORD'S LAW UNTUK MENENTUKAN PRIORITAS AUDIT PAJAK PERTAMBAHAN NILAI

Value Added Tax has contributed significantly in Indonesia’s tax revenue and continually to progress in the term of its role in increasing the tax revenue. Unfortunately, the phenomenon of VAT fraud, intended to minimize VAT payment, would give consequences in violating the tax revenue. In order to minimize this phenomenon, DGT has been maximizing the use of technology in VAT administration. Since the 1st of July 2016, the use of e-Faktur has been enforced to all registered Taxable Entrepreneurs. The enforcement of the e-Faktur has been effectively reducing the number of counterfeit tax invoices. Nonetheless, the e-Faktur is still not be able to capture the accuracy of transactions in Tax Invoices. As a result, DGT relies heavily on the approach of conventional audit for auditing taxpayers’ VAT compliance. This approach is considered to be less effective and become a problem since DGT does not have sufficient tax auditors. The number of tax invoices that needs to be audited could be piled up whilst the amount of tax credits to be audited are also high. This paper aims to discuss this problem by using a statistical technique namely Benford's law. It is recognized in the forensic audit literature that Benford's law can be a tool to help an early fraud examination of many transactions. By using particular statistical procedures, this paper will argue that Benford's Law can be used to analyze the accuracy of VAT value on tax invoices that is reported on the monthly VAT Return.

Implications of Prelecture Material on Cognitive Load and Instructional Effectiveness in Cross‐Disciplinary IS Education: The Nexus of Benford's Law and SQL

ABSTRACTFor some time, there has been a call for cross‐disciplinary teaching within the business disciplines. With the rise of data and analytics, there is an opportunity for cross‐disciplinary teaching by integrating technology throughout the business curriculum. However, many business professors have little experience in cross‐disciplinary teaching. We hope to rectify this by introducing an approach that uses prelecture material to prepare students for learning concepts and terms that are not core to the focal class. In a study that combines Structured Query Language (SQL) coding with an audit principle called Benford's Law, we analyze the impact of adding prelecture material about Benford's Law on student's cognitive load, knowledge gained, and instructional efficiency. Results indicate that students who received a prelecture on Benford's Law outperformed the control group in performance measures related to Benford's Law, and that the instructional efficiency on Benford's Law was also higher for the treatment group. We did not find any significant differences in cognitive load between the two groups, nor did the treatment group perform significantly better when tested on the SQL concepts. We conclude that cross‐discipline teaching is a fine balance between each discipline and communicating to students the importance of both disciplines is key.

FRAUD DETECTING WITH BENFORD’S LAW: AN ALTERNATIVE APPROACH WITH BDS AND CRITIC VALUES

Despite has many critical as much as defenders, Benford’s Law has been used many different ways in accounting. The purpose of the study is to create an alternative standard and critical values that can be used to assess financial data compliance with Benford's law for using as an audit procedure. To this end, the allowable deviation limits were determined on an average basis by analysing the quarterly (20 periods total) balance sheet and income statements of the companies traded in BIST for the years 2013-2017. Analysis done in Excel software by performing 1. Digit, 2. Digit and First 2 Digit tests of Benford Analysis. As a result, a new measuring standard BDS (Benford Digit Score) and conformity limits have been created that evaluated is more effective for audit aims.