Audit numeric data against Benford's Law — the leading digit of naturally-occurring values should follow P(d) = log10(1 + 1/d). Used by auditors, forensic accountants, and election analysts to flag anomalies and fabricated data.
Benford's Law predicts that in many naturally-occurring datasets, the digit 1 appears as the leading digit about 30.1% of the time, while 9 appears only 4.6%. It applies best to data spanning several orders of magnitude (revenues, populations, stock prices, river lengths) and fails for bounded or synthetic data (heights, phone numbers, dice rolls).
The Chi-square statistic tests goodness-of-fit: with 8 degrees of freedom, χ² > 15.51 rejects the Benford hypothesis at the 95% confidence level. The MAD (mean absolute deviation) conformity thresholds from Nigrini (2012) are: <0.006 close, 0.006–0.012 acceptable, 0.012–0.015 marginal, >0.015 nonconformity.