Benford’s Law applied to COVID-19 confirmed case numbers in different countries

Abstract

Benford’s Law states that in sets of random numbers the prospect of the first digit of these numbers being 1 is greater than that of the following digits. Thus, the distribution proposed by Benford’s law shows that number 1 has approximately a 30.1% chance of being the first digit then the digit 2, with 17.6%, digit 3, with 12.5%, and so on, until number 9 is reached, having a 4.6% chance. In this context, the objective of the study is to verify whether this law applies to the numbers of confirmed cases of COVID-19 in different countries. The research, employing a quantitative method, treated and analyzed data collected on the World Health Organization (WHO) website, selecting the following countries, chosen randomly, according to the notoriety received in national and international media: China, Italy, New Zealand, Brazil and the United States of America (USA). To assess the discrepancy between the observed and expected relative frequencies, the frequency comparison test was used. The results found demonstrated that the numbers for China and New Zealand had calculated X² smaller than the critical X², while Italy, Brazil and the USA had calculated X² greater than the critical X², all at a 5% significance level. Consequently, it was concluded that Benford’s Law applied to the numbers of confirmed cases of COVID-19 disease in China and New Zealand, being rejected by the numbers of confirmed cases of COVID-19 disease in Italy, Brazil and the USA.