Benford's Law Analysis

Overview

Benford's Law predicts that in naturally occurring datasets, the leading digit d appears with probability P(d) = log₁₀(1 + 1/d). Digit 1 appears ~30.1% of the time, digit 9 only ~4.6%. Deviations from this distribution may indicate data fabrication or manipulation. Analysis runs in O(n).

When to Use

Trigger conditions:

• Auditing financial data (expenses, invoices, tax returns) for manipulation
• Screening large datasets for data integrity issues
• Detecting fabricated or artificially rounded numbers

When NOT to use:

• For assigned/sequential numbers (zip codes, phone numbers, IDs)
• For datasets with constrained ranges (e.g., human ages, percentages)
• For small datasets (< 500 records — insufficient statistical power)

Algorithm