clear deviation from this benchmark for the second and third digits in nominal market prices with a clear trend towards psychological pricing after the nominal shock of the euro introduction. Genome data The number of open reading frames and their relationship to genome size differs between eukaryotes and prokaryotes with the former showing a log-linear relationship and the latter a linear relationship. Benford's law has been used to test this observation with an excellent fit to the data in both cases. Scientific fraud detection A test of regression coefficients in published papers showed agreement with Benford's law. As a comparison group subjects were asked to fabricate statistical estimates. The fabricated results conformed to Benford's law on first digits, but failed to obey Benford's law on second digits. Statistical tests Although the chi-squared test has been used to test for compliance with Benford's law it has low statistical power when used with small samples. The Kolmogorov–Smirnov test and the Kuiper test are more powerful when the sample size is small, particularly when Stephens's corrective factor is used. These tests may be unduly conservative when applied to discrete distributions. Values for the Benford test have been generated by Morrow. The critical values of the test statistics are shown below: {| class="wikitable" style="text-align:center;" ! ! 0.10 ! 0.05 ! 0.01 |- | Kuiper | 1.191 | 1.321 | 1.579 |- | Kolmogorov–Smirnov | 1.012 | 1.148 | 1.420 |} These critical values provide the minimum test statistic values required to reject the hypothesis of compliance with Benford's law at the given significance levels. Two alternative tests specific to this law have been published: First, the max () statistic is given by The leading factor does not appear in the original formula by Leemis; it was added by Morrow in a later paper. Secondly, the distance () statistic is given by where FSD is the first significant digit and is the sample size. Morrow has determined the critical values for both these statistics, which are shown below: {| class="wikitable" style="text-align:center;" ! ! 0.10 ! 0.05 ! 0.01 |- | Leemis's | 0.851 | 0.967 | 1.212 |- | Cho & Gaines's | 1.212 | 1.330 | 1.569 |} Morrow has also shown that for any random variable (with a continuous PDF) divided by its standard deviation (), some value can be found so that the probability of the distribution of the first significant digit