Background:
“Forensic auditing” opened a new way to monitor demographic data. Benford’s law
explains the frequency distribution in naturally occurring data sets. We
applied this law to data of the world’s population under five. This number is
extremely important in paediatrics and public health. Methodology: Benford’s
law states that the probability of a leading occurring number d (d ∈ {1,···,9})
can be calculated through the following equation: P(d) = log_{10}(d +
1) – log_{10}(d) = log_{10}(1 + 1/d). We compared the observed
and expected values. To examine statistical significance, we used the
Chi-square test. Results: Chi-square for the population younger than five years
is 22.74 for 2010, 22.97 for 2011 and 11.35 for 2012. For all years combined it
is 47.6. Because chi-square was higher than the cut-off value, it must lead to
the rejection the null hypothesis. In 2014 chi-square is 11.73 for the first
digit. Chi-square being lower than the cut off value of the null hypothesis is
accepted. The acceptance of the null hypothesis for 2014 means that the numbers
follow Benford’s law for 2014. The rejection of the null hypothesis means that
the numbers observed in the publication are not following Benford’s law. The
explanations can be reached from operational discrepancies to psychological
challenges or conscious manipulation in the struggle for international funding.
Conclusion: The knowledge of this mathematical relation is not used widely in
medicine, despite being a valuable and quick tool to identify datasets needing
closer scrutiny.

Durtschi, C., Hillison, W. and Pacini, C. (2004) The Effective Use of Benfords Law to Assist in Detecting Fraud in Accounting Data. Journal of Forensic Accounting, Vol. V, 17-34.

Cáceres, J.L.H., García, J.L.P., Martínez Ortiz, C.M. and Domínguez, L.G. (2008) First Digit Distribution in Some Biological Data Sets. Possible Explanations for Departures from Benford’s Law. Electronic Journal of Biomedicine, 1, 27-35.

Suh, I.S., Headrick, T.C. and Minaburo, S. (2011) An Effective and Efficient Analytic Technique: A Bootstrap Regression Procedure and Benford’s Law. Journal of Forensic and Investigative Accounting, 3, 3.

Newcomb, S. (1881) Note of the Frequency of Use of the Different Digits in Natural Numbers. American Journal of Mathematics, 4, 39-40. http://dx.doi.org/10.2307/2369148

Stephens, M.A. (1970) Use of the Kolmogorov-Smirnov, Cramér-Von Mises and Related Statistics without Extensive Tables. Journal of the Royal Statistical Society, Series B, 32, 115-122.