What is Benford's Law in simple terms

(IN) Compliance with Federal Payment Card Spending: A Study of Forensic Bookkeeping Based on Newcomb-Benford Act

CARMO, Pamela Acássia Araujo [1]

CARMO, Pamela Acássia Araujo. (IN) Compliance with Federal Payment Card Spending: A Study of Forensic Bookkeeping Based on Newcomb-Benford Act. Multidisciplinary core specialist journal of knowledge. 03 year, Ed. 06, Vol. 05, pp. 54-78, June 2018. ISSN: 2448-0959



The purpose of this study is to conduct an analysis of compliance in the expenses related to the federal payment cards in 2016, by the law of Newcomb-Benford. The study was carried out by the contribution of articles and publications on the subject, which have proven their efficiency in detecting irregularities in financial data. The methodology for carrying out the work in question can be called hypothetical-deductive, bibliographical research and is based on the technique of quantitative analysis, data in electronic media transparency portal use federal government. The main results show a mismatch with federal government payment cards, in the light of Newcomb-Benford legal editions. The study it can be concluded that there is evidence of the need for better control of public spending through the use of corporate cards.

Keywords: federal government payment card, forensic bookkeeping, Newcomb-Benford law, public spending.

1. Introduction

It is known that when you play a dice, the probability of presenting the number 1 is the same for the other numbers. So what will happen if you have random probability of occurrence of numbers, i. H. the same probability of occurrence for everyone talking about. The law of the NB (Newcomb-Benford) contradicts this hypothesis, the same probability of occurrence for the numbers that are natural as happens when, for example, you bet on a lottery game.

Once the law of the NL was introduced in the midst of bookkeeping authors such as Carslaw (1988) and Nigrini (1999) it was identified as being particularly out there as an efficient tool in detecting fraud and embezzlement in large databases. In research companies and international oversight agencies NB already used extensively in audit software as Audit Command Language (ACL), which features an analysis according to the law of NB, identify the sample data that suggests the need for better research based on statistical reasons .

In the data where it is applicable, if the frequencies do not present the first digits of the data in accordance with the rate provided for in the law of the NB, do not constitute conclusive evidence of manipulation or error, as well as a match not guaranteed trust, but constitute strong indications of fraud or indicates errors in the data that require further investigation.

In detecting the fraud or the socio-economic manipulation that Brazil is speaking of, the need for budget management of public spending is the immediate need and one of the main mechanisms for both, through the acquisition of a control effective. The existing state control mechanisms fail fundamentally through a misallocation of their executives and demand a high price. Using the example of the CPGF expenses (payment of the federal government), which were obliged in irregularities, such as guidelines for the plot-Operation under der Head of the Federal Police (Brazil 2014).

The following problem arises from this research: What will be the amount of the regularity of the payment card expenditure of the federal government, which in 2016, under the optics of Newcomb-Benford?

So the overall aim of this study was to review the level of regularity of federal payment card spending, that is, occurred in 2016, under the optics of Newcomb-Benford.

In order to achieve the overall goal, the following specific goals were defined:

  • Analyze the applicability and efficiency of this tool in the selection of samples to be examined, helping to plan and conduct audits;
  • Try to find out if the expenditures with the CPGF show irregular use and if there is a need for better control over this type of public spending;
  • Introduction of the model to add value to the field of knowledge of forensic accounting and expand the field of the law of the NB

Given the worst recession in the history of Brazil, of course, means must be sought to reverse the negative results and one of the most important factors to be considered is the quality of public spending (MALIK, 2011). The law of the NL presents itself as a forensic tool in investigations justifying this when studying allows a more precise selection of the data, contributing with the examination papers, which has an essential role both in the level of user confidence in information as the economic development of a country and that of the Tribunal de Contas da União-TCU (Brazil, 2016), sometimes takes weeks of work by an auditor with large amounts of data and difficult analysis. In addition to the low cost and effectiveness, the ease of deployment work together.

This work will be presented, in addition to introducing a theoretical framework that will address public spending focusing on CPGF, the law of the NL in a historical context, proposing the methodology to achieve the objectives of the study and the results obtained, followed by the final reflections.

2. Theoretical framework

2.1 public spending

Public expenditure a set of expenditure implemented by public institutions in the calculation of services to society or on investments. Activities for the purpose of buying goods or services are considered processing costs. This processing includes spending and stepping your performance (Rock, 2007).

Public expenditure can only be carried out with the approval of the legislature through the administrative act called public budget and is processed regularly (P, 2008).

Law No. 4.320 / 1964 and LC number 101/2000, state that your implementation goes through the following stages:

  • Appendix: where part of the planning process is available funds (budget recipe) so that they understand that the adoption of measures for situations already idealized observing existing guidelines (LDO-LDO) and priorities of the government (multiannual plan - PPA), manifested by the annual budget law - LOA.
  • Commitment: assigns the resource set for specific, the purposes for which are carried out. Various endeavors can be made, as long as it does not exceed the limit set to make the expenditure. This threshold through the estimates. The execution of the budget so that it is controlled via the aspirations, a schedule for the expenditure with already received and still available funds is possible.
  • Settlement: the settlement of expenses occurs when processing the object of engagement. Provided upon receipt of the goods or services. So the settlement consists of the right acquired by the obligee or the beneficiary for the entrance.
  • Payment: Acquired right by the lender who must prove their claim or enable the beneficiary company to provide payment based on bank transfer documents.

On realization of expenses is also the mode of offering funds that a resource on the server for the payment of an obligation has already acquired, with future responsibility. To ensure progress is still required, the engagement stage with its own foundation and liquidation (BRASIL, 2015). Payment can be made through the federal government payment card, as will be explained later.

2.2 the role of external and internal control of public administration

The democratic regime brings a government activity threshold for this response to the satisfaction of the public interest in obtaining the right common for all. Noting that the cause did not succeed the government, but rather society as a real concern of your good management, it is up to you to preserve the people. The entry for management to a control will prevent the order, to ensure that it is enshrined in its right to a good and effective presentation.

Cochrane (2003) says that in the context of public administration, budget control execution is exercised due to legal restrictions in order to verify if the actions of his servants have been executed with legitimacy and, above all, in accordance with the public interest. This control takes on one of two types: internal and external control.

Internal control "is the set of procedures, rules and objectives of internal management to comply with the administrative policy of the organization, trust in the effectiveness and efficiency of resources" (AICPA, 2017 p. (1). It is established by the executive branch with the Central Office Ministry of Transparency, Supervision and Office of the Comptroller General, where your expertise includes all federal executive bodies, with the exception of industry associations, also the external control function in providing useful information.

The external control is the control by a unit that integrates the same organizational structure and does not monitor the organ. The aim is to monitor the actions of the executive in the use of public funds. Legislative energy is held in the office of the National Congress, with the help of the Tribunal de Contas da União-TCU in the Federal Gazette and in most cases the state courts of the Auditor-TEC for the states and municipal audit offices - TCM for municipalities (SA NTANA, 2014) .

In the public administration control is then the possibility of the test, inspection and examination by oneself, by other powers or by every citizen to carry out the effective correction of the administration, one power organ or on the threshold authorized to guarantee the achievement produce as desired and previously planned a systematic conference (Krieg, 2003).

2.2.1 Public Spending Control Tools

The administrative control is exercised by technical and qualified specialists in the administration and record the actions of the public administration and thus information from those who compete are monitored.

The internal control is directed to ordering the records of the actions of the government, presented as an essay as statutory 64 / 4,320:

I - the legality of acts that result in the listing of income or expenses, the birth or extinction of rights and obligations;

II - functional fidelity of government agents responsible for goods and public values;

III - the fulfillment of the work program in financial terms and in terms of the execution of construction works, as well as the provision of services expressed.

External control is already monitoring such practices in the areas of accounting, financial, operational and financial assets. Evaluate the development of expenditure in real time also a control is exercised in parallel with the execution of the budget, setting limits to inhibit the disorderly increase in expenditure, suggesting corrective measures and the detection of mismanagement, corruption and administrative misconduct.

Aspects such as quality, suitability, effectiveness and satisfaction of the citizens, of the goals that are achieved by the managers are also controlled. Prohibition managers who want to use opportunities for privileges or discrimination (VIRGILIO, seek 2011, p. 13).

For the calculation of the expenses by the CPGF, this is considered a possibility of internal control of these expenses, "since it allows the setting of the limit values ​​on the basis of the specified parameters as well as the monitoring of the actual expenses through the invoices of the cards" (CAMPOS, s . 39, 2006). And the external control is subject to later, too.

2.3 Federal Government Payment Card-CPGF

The Federal Government Payment Card-CPGF "is a means of payment used by the public administration in order to give the administration more flexibility, control and modernity in the management of the resources" (NATIONAL TREASURE, p. 4-2017).

Aimed at the use of UG management units by the federal government and foundations. Expenditures for the purchase of materials and services through CPGF, only framing those as delivery of funds.

Subject purpose to serve, small purchases of goods and services payment and immediate delivery, framed as supply of funds, in affiliate institutions (art. 45, 46 and 47 decree nº 93.872 / 86), which may entitle other expenses established by the law Minister of Finance and Planning, Budgeting and Management "under the sole paragraph of Art. 10 of Regulation No. 2005 / 5.355 (COMPTROLLER GENERAL, 2017, p. 4).

The execution of the expenditure by providing funds differs from other forms of execution of the expenditure for the commitment on behalf of the server, the progress and the amount made and the lack of mandatory offer. For the implementation of such expenditures, the principles of public administration as legality, impersonality, morality, publicity and efficiency as well as the principle of equality and the acquisition of beneficial ones are to be observed by the administration (COMPTROLLER GENERAL, 2017, p. 5).

Are responsible for managing these resources, the cost of computers each unit manager-UG.

Should be provided accounts delivered, within the time limit according to the law of granting of supplies that you receive. If there is no accountability within the set deadline, or it contains errors or irregularities, the author of the expenditure should immediately inform him to introduce accountability, correct the error or reduce the treasury account values ​​according to national registrations as unethical, on the payroll The agent always supplies the special account or the discount if you do not respond to notification of the appropriate importance.

In Table 2 below, which CPGF expenses have suffered significant increases over the past 15 years can be clearly identified. The development of expenditure was carried out on the basis of the total expenditure for 2002.

2.4 Newcomb-Benford Law

Simon Newcomb (1835-1909), a Canadian-American astronomer and mathematician, noted at the end of the 19th century that the books of tables of logarithms contain higher wear due to use on their pages where the first digit of the logarithm with smaller ones Numbers like 1 and 2 began, and such deterioration was significantly higher than in the pages where the logarithms began with a larger number like 8 and 9.

Her comment was published in the American Journal of Mathematics, 1881, reference to the HaThe frequency of using the various digits in natural numbers has been publishedt. And it occurred as "natural numbers" occur "in nature", that is, the numbers that arise in normal everyday life without preconditions or manipulation.

It is clear that hardly anyone would be interested in a table of logarithms; however, this question can be given greater importance to study when one considers that these tables are used in the construction of scientific literature, engineering, and others that are available. Property discovery and presented is expressed by Figure 1 below:

For a set of data to be considered punishable by law test of NB, its values ​​must represent the extent of the event or fact; the data set cannot be small or contain small variations. In this context, it has been rigorously shown by Hill (1996) that the distribution of the distribution of random numbers collected from a variety of different distributions follow the distribution of the NB

Newcomb (1881) and Benford (1938) explained that in nature there are other numbers starting with digits of the smallest value and explanation of the statute of limitations aimed at the result of the scarcity of natural resources. What would have remained as a mere mathematical curiosity became useful by Benford, an investigative journalist, when viewed as numerical balances and statistics (Rock, 2007) in the discovery of fraud in large quantities.

Nigrini, one of the forerunners of the NB law enforcement agencies in the midst of accounting, got so based on your Ph.D thesis in financial accounting (Ceccato, 2013). He suspected that real data would result from the law of the NB, and your research has shown, precisely in this way, that significant deviations in relation to the law designating or producing the possibility of fraud. He developed tests to measure compliance with the NB's laws and detected they amounted to in seven New York companies. The discovery was reported by the Wall Street Journal and Nigrini was asked to advise the tax authorities in various countries with mention of the incorporation of the NL into fraud detection software.

It is worth noting that the tools for analysis under the law of the NB, including software, do not prove the existence of fraud, manipulation or errors, only to identify data that deserve your further investigation. Durtschi (2009, p. 23) makes it clear that "Existing digital analyzes should not complement other tools and should not be used alone.

In Brazil, Santos at al. (2007) the applicability of the model is based on Newcomb-Benford's law in the process of auditing the ISS in the northeastern city signaling any discrepancies with the issuance of tax accounting notes, which were confirmed by the results of the monitoring carried out.

Ceccato (2013) presented a study on the look of the legal NB civil engineering budget worksheets for the analysis of mark-up. We are analyzing the construction of three stadiums for the 2014 World Cup, including the Mané Garrincha, to check their applicability in this context. The results were compared with the results of the test by TCU, achieving the same results in both methods indicated too expensive.

On the coast. Al (2013), conducted a study to assess the applicability of the law in places of continuous examination law analysis of the NB in ​​the engagement of administrative state units 60 northeast of 2010. In the results in the realization of a temporal analysis of compliance with the law, the ability to determine with greater precision items of interest observed in the formation of samples applied in light of law and in an audit environment was still highlighted.

Through this work then an analysis on Government Payment Card Expenditures (CPGF), consider the tools presented in this context are already being used in the identification of possible deviations.

3. Methodological process

For the scientific method, it was assumed the hypothetical-deductive, Karl Popper (1975) Apud Gil (2008), if knowledge is insufficient to explain a phenomenon, then a problem arises; to express the difficulties of the problem are formulated hypotheses; Case will be deducted follow that are tested or falsified, looking for empirical confirmation or if you reject a hypothesis.

As the problem of research, then a null hypothesis and an alternative where the null hypothesis (Ho) becomes an act of NB was established

The survey is based on a quantitative approach, descriptive, since sought to analyze registers and a particular phenomenon (compliance in the distribution of the first digits of the CPGF costs in relation to the distribution defined by the NB) -correlated to describe them and their characteristics.

It served as a means to bibliographical research, based on books and scientific articles already published, as well as Excel tables containing the CPGF editions for the years 2016, in the portal of the Federal Government Transparency in Middle Electronic (www.portaltransparencia.gov.br/).

The NB Law has been applied to the data in the way that it was originally presented. The database does not go through any prior treatment as it was made available through the portal. This determination was represented by the fact that the law governing the selection of items in a database that could contain errors, were manipulated or Fraldes and obtained results represent the sample for testing.

This study was inspired by the work of Chan (2015), who conducted her research on federal government expenditures in 2013. As a limitation of the research documents the object of the analysis data were received on presentation, which happened in accordance with the law transparency through a web portal, not original certifying security and trustworthiness to the data.

The following presented the tests that were applied, highly regarded and recommended second Nigrini (2012), for testing the actual frequencies found-data-compared to the expected frequency of the digits provided in this law.

3.1 test the first digit

The first digit is a primary test and found for checking the frequencies on which the numbers 1 to 9 occurred in the first digits, expenses, the analyzed data where the expected frequency of occurrence of a number as the first digit According to the law of NB is given by:

So, to:

n = 1, P (n = 1) = log10 (1 + 1/1) = 0.301 = 30.1%,

n = 2, P (n = 2) = log10 (1 + 1/2) = 0.176 = 17.6%

n = 3, P (n = 3) = log10 (1 + 1/3) = 0.125 = 12.5%


d = 9, P (d = 9) = log10 (1 + 1/9) = 0.046 = 4.6%

Test the first two digits 3.2

The first two digits test was performed to identify the frequency of the first two digits of the real data, compared to the expected frequency of the number D2 = d2, as the second digit in a series of values, since the first digit D1 = d1. According to the law of the NL, this frequency is given by:

This test was also carried out by Nigrini (2012) for the analysis of large databases, for it more precisely than the previous test suggested. Here, a low compliance with the NB Act usually suggests a high risk for the existence of errors or fraud.

3.3 Average of the absolute deviations

The test for the mean absolute deviation (MDA) was carried out to measure the deviations statistically and was used, among other existing tests for by Nigrini (2012) for large databases, as it ignores the size of the database. Its calculation is done as follows:

Where "K" is represented in the series of digits, for example, nine for the first digit, PR = actual ratio and PE = expected ratio. The average absolute deviation is an important test to be applied because, unlike the variance and the standard deviation, dispersion in your metric data does not suffer high mixed influence in the distribution. There are no critical values ​​for this test. Nigrini and Dunkel (2000), through Newcomb-Benford's personal experience of examining databases, Guidelines on Critical Values.

Table 2-Critical Values ​​Suggested for Average Absolute Deviation

First digits0.000 0,006Approximate match
the 0.012 0.006Acceptable compliance
the 0.012-0.015Marginal compliance acceptable
Above 0.015Discordance
Second digitsthe 0.008 0.000Approximate match
the 0.010 0.008Acceptable compliance
0.010 to 0.012Marginal compliance acceptable
Above 0.012Discordance
First two digits0.0000, 0.0012Approximate match
the 0.0018 0.0012Acceptable compliance
the 0.0022 0.0018Marginal compliance acceptable
Above 0.022Discordance

Source: adapted from Nigrini (2012)

3.4 total test

Nigrini (2012), by simulating distributions under the optics of Newcomb-Benford, found that the total number belonging to the individual groups formed by the first two digits, 10, 12, 11 ..., 99 resulted in values ​​on a proportion from 1/90, d. H. roughly equal totals for each group. Soon, this test consisted of the sum of all the numbers, per group, that had been formed in accordance with their first digits.

The author also found that real numbers rarely follow this proportion because only a few very high values ​​and the remaining or a lot of small or medium value values ​​mixed up. The application of this test is precisely for a warning about this fact. Analyzed data groups should present different proportion of the expected, being, from 1/90.

4. Results and data analysis

The data in the portal of the Federal Government Transparency, 114077 CPGF expenditure were identified in 2016, the analysis of which is carried out below.

4.1 Analysis of the first digit

The following table shows the frequency distribution of the data in relation to the expected frequency, given the NB law for the first digit.

The result of Diagram 1 shows that the distribution of the data in a downward curve analysis as well as suggests the distribution of NB, the probability of occurrence of the first digit.

Table 3 shows that the test result of the mean absolute deviation (MDA) given the actual frequencies reaches the first digit.

Table 3-MDA for the first digit of the expenditure with CPGF


Source: own elaboration. MDA = 0.004

The actual frequencies the first digits of each spent on CPGF presents a proximity to the sales, the law of the NB established The digits 3, 6 and 8 have exactly the rate provided in the law. About the deviations in the other digits, the result of the test found for the average absolute deviation (MDA = 0.004), shows an approximate compliance data in the analysis.

4.2 Analysis of the first two digits

The following table 2 shows the frequency distribution of the data in relation to the expected frequency, given the law of the NB, for the first two digits.

In addition to the previous test result, it offers the actual frequency downhill. The peaks of the digits 10, 20, 30, 40, 50, 60, 70, 80 and 90 indicate the need for better evaluation of the same.

the following table shows the results of the mean absolute deviation (MDA) given the actual frequencies reached the first two digits 4 instead of to ensure the need to evaluate the digits that have shown higher graph 2 deviating from above.

For the test of the first two digits, digits 12, 16, 18, 19, 55, 78 and 99, showed exactly the frequency expected by the law of the NB But here the remaining numbers show a slight deviation between 0.005 and 0.001, the average absolute Deviation presents a non-compliance with the law of the NL

4.3 total test

To analyze the test results of the sum together with the test results of the first two digits, put the amount of data in each group with the sum of the values. In order to identify the relevance and materiality of each group digits that suggest the need for a more in-depth analysis about these values, they are identified.

Chart 3 below shows the test result totaling on CPGF expenses.

the table below shows the results of the sum, detailing to ensure the need to evaluate the digits that have shown higher diagram 5 differ 3, above.

The test of the sum for your time, recognized a significant discordance in the light of the law of the NB, with values ​​in relation to the expected average 165% above the value of 1/90 and below the proportion only 10% expected average of the value. The digits 10, 15, 20, 60, 72, 75, and 80 represent the most significant digits in this test. In an audit, the first would be singled out for a more in-depth analysis of the test for the first two digits.

It was said during the work that in accordance with the law of the NB results inconclusive irregularity, but evidence that the need for better analysis of the same to assume. When analyzing payments numbers, the numbers that indicate when tested with a higher level of nonconformance in the sum test (Table 12) than digits 10, 15 and 80, presented some high value transactions or many low value transactions that this requires depending according to model, a deepening in analysis.

With the end of the example for this model, sought a more detailed initial identification of the possible reasons for discrepancy, looking for evidence that paragraph 10-related irregularities could include issues that have contributed to number controls with greater relevance to the discrepancy the Newcomb-Benford law.

Table 6 - Analysis of the composition of expenditure began with the number 10.

fate Total per travel destinationquantityRelationship with overall general
ClassifiedR $ 436.503.061517 %
preyR $ 208.616.158498 %
fuelR $ 577.953.24134022 %
Supermarket / bakeryR $ 134.617.334695 %
Restaurant / snack barR $ .34 183.3232337 %

Source: Portal of the Federal Government Transparency, adapted.

Outside of this legal use contextualized inflowing funds by the CPGF, you do not configure the rule, but the exception. Identified in this analysis, as described in the table above, were presented when the expenditures significantly large arise in a common fate. In order to use CPGF, you need to identify the impossibility of submitting such expenses to normal application, in addition to costs that are repetitive in nature not due to the supply of funds that were once considered foreseeable funding therefore do not justify your specificity.

For funding through this mode of payment of expenses are identified both the lack of contractual coverage, how to recognize that it is not the same object / signings interruptible service plan, so, along the exercise is not considered fractionation of costs and consequently the tender required to be characterized.

Without exception, also to mention the amount of the disbursements, you could not identify the nature of the costs and are only allowed in exclusive cases where, in addition to the peculiarity of the costs, there is a justification for your use, when the expenditure through the delivery of funds should preferably mean Invoice. The use of the incoming funds can only be done through withdrawal if the payment is not made by the CPGF, which can happen in a single supplier, the machine for the use of the card is not possible.

The manual of the CGU, brings clarity about the use of CPGF, still warning that its use should not be kept in the calculation of expenses with restaurants, events, or in the purchase of food for the preparation of their own division or from it, with ready meals You will be for the supply of funds.

Also wanted to analyze what could spend, with even more critical ones, because of the large amounts of expenditure for a similar supplier when costs were identified, which are presented in Table 15 below.

Table 7 - Analysis of the composition of expenses began with the 10-digit from fate.

Unit Manager-UGsuppliervalue
ADM International Department m.d.NAU seafoodR $ 1,000.00
11. ReservoirRestaurant jeriváR $ 109.11
Logistics Battalion 5Palhoça restaurantR $ 1,000.00
Comp-Rec-Minerals ResearchBamboo coconut teresinaR $ 100.00
Ministry of DefenseMC DonaldsR $ 108.00
ADM and Basis support cmnCocoa showR $ 1,000.00
5th Supply BattalionThe CLA choppR $ 1,000.00
ACAD Militar Das Agulhas negrasRoots barR $ 1,000.00
Rincao StudPull-up barsR $ 1.038.58
Army commandBar popsiclesR $ 109.10
Army commandBoulevard beer, beer barR $ 109.07
Ministry of DefensePigalle bar night clubR $ 108.00
Base and support cmnPit Bull original jeansR $ 1,000.00
Base and support cmnSanchez jewelryR $ 1,000.00

Source: Portal of the Federal Government Transparency, adapted.

When viewing the expenses table 7 above, first identified the values ​​of the expense limits spent by CPGF. And all of the costs raised above by your property suggest the need for a review, if not as an eligible expense, through a funding on allocation of funds based on the following assumptions:

  • Small purchases of goods / services that require ready-service and immediate delivery for service to the common good;
  • Expenses related to the activities of the unit, such as in the public interest;
  • Expenses for alcoholic beverages, both in the locality instead of in which the organ is located as outside, are considered ineligible, in other words, cannot be paid for with public funds, except for official receptions.

Final considerations

The present study aimed to evaluate the model based on Newcomb-Benford's law applicable to the work of overseeing public spending, spent with the federal government payment card-CPGF, in order to identify a more practical method low-cost, the audit- Procedures are taken into account, improve and contribute to better management of public spending that is necessary.

This study in your proposal to the Newcomb-Benford Act as this tool to prove that can contribute to a greater efficiency of the control of the public expenditure audit identifies possible irregularities in the financing of the expenditure for the CPGF especially when excessive expenditure repeatedly identified the same nature, and the legality of your use is exceptional and has potential.

The high growth in the calculation of expenses considered by the CPGF, marked the quiet, made clear the need for efficient control and with clear goals and the effective range.

Results obtained showing statistically significant deviations in relation to the expected frequency according to the law of Newcomb-Benford, lead to the rejection of the null hypothesis, which indicates agreement with the expenditure CPGF. It is believed that the results of non-compliance, fraud or irregularities do not confirm, but that the results presented here indicate that more detailed research into such issues, indicating the existence of a likely ineffective control.

It is recommended that you apply the unit-basement manager model, with the application of statistical tests such as the Z-tests and Chi-Square, when these are indicated for use in small databases.


AICPA, internal controle, 2017. Available: accessed: 14 May. 2017.

BENFORD, Frank. The law of anomalous numbers. Proceedings of the American Philosophical Society, Vol. 78, No. 4, 1938.

Brazil. 4.320 Law of March 17, 1964. Available: accessed: 23 Apr 2017.

Brasilien, Supplementary Law 101 of May 4, 2000. Available: accessed on: 25 Apr 2017.

Brazil, InovaTCU: Applications of Benford Public Works Act audit 31 jun. 2016. Available in in access : 27 jun. 2017.

Brasilien, the supply manual (theoretical part), 16 10. 2015. Available: accessed: 15 May. 2017.

Brasilien, the transparency of the Bundesreyaw, 2017. Available: ​​accessed: 23 Mar 2017.

Brazil, portal. Federal Police: B.Combating fraud with the MT Corporate CardE, 28 Mar. 2014. Available in access : 29 May. 2017.

Fields, Marcus Aurelius. Transparency of federal spending: external control over the funds invests through the provision of funds2006. 96 See Monograph of Specialization in Public Accounting, Graduate Program Serzedello Corrêa Institute of the TCU in partnership with the University of Brasilia.

CARSLAW, Charles. A. p. N. Anomalies in Income Numbers: Evidence of Goal Oriented Behavior. The Accounting Review, United States, Vol.LXIII, No. 2, pp. 321-327, Apr. 1988.

CHANDRA, Gustavo Henrique de Vasconcellos. Law Enforcement Newcomb-Benford in Identifying Irregularities: The Example of Federal Payment Card Spending. The Central Bank Attorney General, Vol. 9, No. 1.2015.

CECCATO, Flávia r. c. Nowcomb-Benford Law Public Works Supervision Applicationsn. 2013. 486 f. Dissertation (Master). Faculty of Economics, Administration and Accounting, University of Brasília, Brasília. 2013.

CGU, Federal Government Payment Card Manual, 2017. Available: accessed: 29 Apr < / http:> 2017.

Cochrane, Therese M.C The BeInterpretation of the internal control system in the Brazilian public administration and accounting Contribution as the main instrument of control in tracking the efficiency of the public administration. 2003. Work, 21 see IX Bookkeeping Convention of Rio Grande do Sul.

COSTA, José de Freitas on Isídio. Al. Analysis of compliance in public expenditure of the Federal elements: Law enforcement Newcomb-Benford during the first and second digits of the expenditure in two Brazilian statesn. 2013. 12 p. r. Cont. Fin.-USP, São Paulo, v. 23, n. 60, s. 187-198, s. 10. 2013

DURTSCHI, Cindy, on. Al. The effective use of Benford Law to aid in the detection of fraud at the end of the yearG. Journal of Forensic Accounting, V. 5, pp. 17-34. 2004. Available at: . Accessed in: April 15, 2017.

GIL, Antonio Carlos.Methods and techniques of social researchG. 6th Ed. São Paulo: Atlas, 2008.

GAMST ST.JAMES, A. C .; RAMIREZ, F.. Composition of public spending and economic growth: A macroeconomic assessment of the quality of public spending of the Brazilian states. Applied Economistsschaftslehre, Vol. 11, No. 4, pp. 463-485, 2007.

War, Evandro Martins. External and internal controls of the public administration and courts of the accountsn.Belo Horizonte: Forum, 2003.

HILL, Theodore p. Bas e-invariance means Benford Gesetz, proceedings of A. m. s. 1996, USA, Society Vol. 123, No. 3, pp. 887-895.

IBGE, IPCA / INPC consumer price index, available at: accessed: May 12. 2017.

MALIK, Raquel Fernandes. Quality of public spending, investment in transport infrastructurer. 2011, 49 p., Placement Reports to Get a Masters Degree in Economics and Politics, Lisbon,

NEWCOMB, Simon. Freqwency of the use of the Differelnt Digits Im Nuw Natural & Ers. American Journal of Mathematics, Vol. 4, No. 1. (1881), pp. 39-40.

NIGRINI, Mark. J. I've got your number. Journal for billingWesen, Ny, Vol. 187 inch-5, pp. 79-83, May. 1999.

NIGRINI, M. j. Benford Law. Applications for surveillance, forensic accounting and fraud detection. John Wiley & Sounds, New Jersey, 330 p. 2012.

Mark j. NIGRINI & dark, s. J. Theretum diagnostics using second-order tests from Benford's law. MonitoringG. The Journal of Practice & Theory, Vol. 28, No. 2, pp. 305-324. November 2000.

Paiva, Simone Bastos. A discussion of the non-definition of publichen spending in the field of public accounting lawsee Brazilian Accounting Magazine, Brazil, No. 171, May. 2008.

SANTANA, Ariel Santos. The external control of the public administration in Brasilien 2014. Available: accessed: 23 May 2017.

SANTOS, Michela, et al. Applications of Newcomb-Benford's Law to Tax Audit of Tax on Services of All Kinds (ISS). Bookkeeping Magazine, Vol. 20 Finance &, para. 49, 2007.

NATIONAL TREASURE, Handbook of the Federal Government's Payment Card, 2017. Available at: accessed on 30 Apr 2017.

VIEIRA, Alessandra da Silva. The right of Newcomb-Benford as a sample selection criteria in the tax auditG. CAD. Fin.Public, Brasilia, n.14, 139-167, p.10.2014

Virgilio, Salman Vieira. Control and transparency as tools to combat crimes committed by public administrationG. 2011. 17 see lecture at the 1st competition of scientific works of ASBAN and JUNIOR / go.

[1] Accounting course at the Centro Universitário de Brasília (UniCEUB).