EZ-R Stats, LLC

Benford's Law does not apply to all numeric populations.  In particular, the following areas should be considered before testing a population for conformance with expected distributions as predicted by Benford's Law:

1. All of the transactions should measure the same attribute, i.e. all are dollar values, lengths, counts or other numeric attribute.
2. There should be no established minimum or maximum value.  For example, a population of small purchase orders, defined as being between $100 - $500 will not necessarily conform to an expected distribution.
3. The numbers should not be pre-assigned numbers, they should be random in nature.  For example, a pre-established range of checks for one month starting and ending with a fixed number is not a candidate for analysis.
4. There should not be a “clustering” of values around a particular amount.  For example, if charges for a pharmacy prescription are clustered between $9 and $12, the distribution should not be expected to conform with Benford's Law.

Generally, the measure of conformity of any distribution can be compared with the expected distribution and the conformity can be measured by computing the “Chi Squared” value and then looking up the value in a table of probabilities to determine the likelihood that any difference is related to chance alone.  Often, the auditor will find that an analysis of conformity with Benford's Law will yield results that clearly indicate conformity vs. non-conformity.  For example, an analysis of conformity of certain census data with Benford's Law shows that the probability that any differences are due to chance is more than 95%. Further, Chi Square results are generally not reliable unless each expected value is at least five.  This means that the size of the population needs to meet a certain minimum value, depending upon the type of test being performed. Also, the data being analyzed should consist of at least four digits, otherwise there may be a bias towards the lower digits.