TITLE:
The World’s under Five Population—Do We Really Have Good Data of Its Size in Medicine?
AUTHORS:
Gregor Pollach
KEYWORDS:
Benford’s Law, Forensic Auditing, Under Five, Struggle for Funding, Fraud, First-Digit Law, A New Tool in Medicine
JOURNAL NAME:
International Journal of Clinical Medicine,
Vol.5 No.10,
May
23,
2014
ABSTRACT: 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) = log10(d +
1) – log10(d) = log10(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.