Do Redlisted Species Follow Benford’s Law?

Abstract

Benford's law describes how different numbers are distributed as first figures in statistics. The law states, for example, that the number 1 should be the first digit in 30.1% of cases, the figure 2 in 17.6% of the cases and the figure 9 in 4.6% of the cases. If Benford's law is violated, it may be an indication that the numbers may be manipulated, or more generally of low quality. Possibly the most high-profile case is the investigation of the Greek macroeconomic accounts. The Stability and Growth Pact of the EU imposes certain constraints on member countries budget deficits, and there were concerns about the Greek economy in the 2000s. According to some observers, it was well-known among EU-officials that the Greece numbers were cooked. It is then of some interest to note that the Greek macroeconomic data were those that showed the most significant deviation from Benford's law, compared to all other EU-countries, according to the analysis of Rauch et al (2011). Analysis of the law has used different data sets: Sandron (2003) studies the population of 198 countries (good agreement); Ley (1996) finds that one-day returns for some American indexes follow the law; Gonzalez-Garcia and Pastor (2010) shows that macroeconomic data generally follows Benford's law. Nigrini & Mittelmaier (1997) produces a test for accounting fraud analysis. According to Stigler's (1980) law, the name of the discoverer is often different from the name of the law; it is seemingly widely acknowledged that Newcomb (1881) already made the discovery. Fellman (2014) provides a comprehensive review of the literature. Intuitively, the law does not work well for certain types of data, such as length of humans, where the majority of the numbers start with 1 and a few with 2. We must also have a large data base, so that we have enough variation in the data. It is not a very intuitive law, although there are some attempts to show that the law follows from certain mathematical arguments. Our approach here is just to apply the law to a certain data-set and explore whether or not it holds true. The law does not prove that the quality of data is bad, but it is sufficiently well tested in so many contexts that a deviation from the law merits a closer investigation of the data generating process.