Test Of Benford’s Law (BL) and Approximate Distribution on Bl-Ready Disbursement Voucher (DV) Amounts

Rhenozo Barte

Rhenozo Barte University of the Philippines Cebu

Keywords: Benford’s law, digital analysis, fraud audit, numbers pattern

Abstract

Digits of natural numbers were thought to occur uniformly until Simon Newcomb and Frank Benford separately observed in 1881 and 1938, respectively, that 1, as the leading digit, occurs more frequently than 2; a leading 2 occurs more frequently than 3; and so on. It became the famous Benford’s law (BL), which has been used in auditing, accounting, and natural and social sciences.

This work tests such qualities on disbursement voucher (DV) amounts, with a prior knowledge that the audit report finds it neutral or free from bias or manipulation. DV amounts include all sorts of disbursements, making the data set a rich ground for demonstrating the procedures for BL. While it is widely used in auditing, Reports using BL as a base of research work is still scant in the Philippine setting, much less in a localized one such as Cebu City; thus, the choice of this particular data set somehow attempts to close the gap.

From 2,355 raw DV amounts in 2014, procedures further reduced the data points (N=1,237) to satisfy the conditions for the first and second digit tests on both the original distribution and the difference of the ordered statistics whose cumulative distribution function, its proponent claims, is within 3% of BL.

Results of the first digit test using chi-squared, mean absolute deviation, and OLS show that BL-ready data manifest a behavior that conforms to the BL distribution at 95% and 99% level of confidence. Moreover, the second digit and second-order test results corroborate the initial findings, implying that the data set conforms to the BL distribution. Procedures further show that using raw or original data alone may lead to inconclusive or even inconsistent results. Thus, this study recommends a careful readying of data for the BL test, which offers particular benefits to auditing and accounting. Furthermore, it is recommended that the methods employed here and others be used in data sets with adverse audit reports.

Author Biography

Rhenozo Barte, University of the Philippines Cebu

Rhenozo Barte is a university instructor at the University of the Philippines Cebu, handling courses such as Basic Accounting, Managerial Accounting, and Financial Management. He obtained his master’s degree from UPV Cebu College and his BS Accountancy Degree from UPV Iloilo campus. He worked for a few years (1999–2002) as an accounting supervisor at EMI Philippines, Inc. He also spends his time doing social work and giving leadership talks on topics such as time management, work-life balance, and financial management. He is currently pursuing a Ph.D. in Business Administration.