results, suggesting widespread ballot stuffing. Another study used bootstrap simulations to find that the candidate Mehdi Karroubi received almost twice as many vote counts beginning with the digit 7 as would be expected according to Benford's law, while an analysis from Columbia University concluded that the probability that a fair election would produce both too few non-adjacent digits and the suspicious deviations in last-digit frequencies as found in the 2009 Iranian presidential election is less than 0.5 percent. Benford's law has also been applied for forensic auditing and fraud detection on data from the 2003 California gubernatorial election, the 2000 and 2004 United States presidential elections, and the 2009 German federal election; the Benford's Law Test was found to be "worth taking seriously as a statistical test for fraud," although "is not sensitive to distortions we know significantly affected many votes." Benford's law has also been misapplied to claim election fraud. When applying the law to Joe Biden's election returns for Chicago, Milwaukee, and other localities in the 2020 United States presidential election, the distribution of the first digit did not follow Benford's law. The misapplication was a result of looking at data that was tightly bound in range, which violates the assumption inherent in Benford's law that the range of the data be large. The first digit test was applied to precinct-level data, but because precincts rarely receive more than a few thousand votes or fewer than several dozen, Benford's law cannot be expected to apply. According to Mebane, "It is widely understood that the first digits of precinct vote counts are not useful for trying to diagnose election frauds." Macroeconomic data Similarly, the macroeconomic data the Greek government reported to the European Union before entering the eurozone was shown to be probably fraudulent using Benford's law, albeit years after the country joined. Price digit analysis Benford's law as a benchmark for the investigation of price digits has been successfully introduced into the context of pricing research. The importance of this benchmark for detecting irregularities in prices was first demonstrated in a Europe-wide study which investigated consumer price digits before and after the euro introduction for price adjustments. The introduction of the euro in 2002, with its various exchange rates, distorted existing nominal price patterns while at the same time retaining real prices. While the first digits of nominal prices distributed according to Benford's law, the study showed a