12. The Procedure — Running the Test Yourself

The Preliminary Assessment

A researcher must begin by checking the range and the mantissa spread of the data before applying any mathematical expectations regarding digit frequency. R.M. Fewster in 2009 established that these properties provide the necessary foundation for any analysis, as seen in the method described in her paper. In 2026, the AICE institution applied this logic to three distinct datasets, specifically measuring Fibonacci numbers, 132 rivers, and 195 countries' mean heights. These measurements confirm that the span of the data determines whether the test is even applicable to the set in question before proceeding further. Failing to verify the mantissa spread invites error, as the distribution is not a universal law but a property dependent on specific data characteristics. By evaluating these metrics first, one avoids the common mistake of assuming that all numerical data must conform to the expected logarithmic distribution.

The Necessity of Unit Variation

The procedure demands that the test be run in more than one unit to ensure that the findings are not merely artifacts of measurement. As demonstrated by AICE in 2026, testing the three datasets across six length units revealed how sensitive the leading-digit output is to scale. The Fibonacci numbers showed close conformity with a KS 0.0106 distance, remaining stable across every unit and base tested during the experiment. Conversely, the 132 rivers with a KS 0.3764 and 195 countries' heights with a KS 0.7357 both displayed clear nonconformity in every unit used. For those failing sets, the leading-digit answer shifted whenever the unit changed, providing concrete proof that a single-unit test proves nothing on its own. An investigation that relies on a single set of units ignores the possibility that the apparent pattern is an illusion created by the scale.

The Interpretation of Results

Conformity is not an absolute proof of truth or accuracy, but merely an observation that the data follows a specific mathematical regularity. No serious dispute exists regarding these findings, as the distinction between conforming and nonconforming datasets is supported by the rigorous 2009 method. One must treat the result as a question to be investigated further, never as a final answer or a definitive judgment on the data.

Example: A ruler that changes length depending on the temperature is a poor tool for measuring the structural integrity of a bridge.

Verdict. A test result is only as robust as the variety of units used to confirm its stability across different scales of measurement.

Overturned if: A dataset currently marked as nonconforming, such as the 195 countries' mean heights, were to show consistent conformity across all tested units.

Sources. 2009 · R.M. Fewster, "A Simple Explanation of Benford's Law" — PDF · 1999 · Mark J. Nigrini, "I've Got Your Number" — Journal of Accountancy