The World’s under Five Population—Do We Really Have Good Data of Its Size in Medicine?


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.

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Pollach, G. (2014) The World’s under Five Population—Do We Really Have Good Data of Its Size in Medicine?. International Journal of Clinical Medicine, 5, 599-604. doi: 10.4236/ijcm.2014.510081.

Conflicts of Interest

The authors declare no conflicts of interest.


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