Friday, November 6, 2020

Something That I Never Would Have Thought Possible

 What is Newcomb-Benford's Law?

Benford's law, also called the Newcomb–Benford law, the law of anomalous numbers, or the first-digit law, is an observation about the frequency distribution of leading digits in many real-life sets of numerical data. The law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.[1] For example, in sets that obey the law, the number 1 appears as the leading significant digit about 30% of the time, while 9 appears as the leading significant digit less than 5% of the time. If the digits were distributed uniformly, they would each occur about 11.1% of the time.[2] Benford's law also makes predictions about the distribution of second digits, third digits, digit combinations, and so on.

This page lets you test the law against various data sets.

4/1/2017 Journal of Accountancy shows how to use this to look for fraud. (I suspect that if you look at total monthly sales, and the first digit is distributed in the 11.1% distribution, you may want to dig a bit deeper into the books.) So what?  Here is a collection of data using Newcomb-Benton Law to analyze precinct returns.  While many conform to the rule, others are suspicious.  The red lines are expected frequencies:




When you are making up numbers out of your head, you do not even think of Newcomb-Benton Law, and so you produce results that satisfy your inner Democrat, but do not map well to the real world.



4 comments:

brian said...

"...your inner Democrat." Hilarious!

brian said...

"Testing Benford's Law" is a very cool interactive bar-graph plotter with a dropdown box of a couple of dozen real-world datasets to graph as test case. The Fibonacci numbers leading-digits distribution is virtually a perfect fit:

https://testingbenfordslaw.com/first-652066-fibonacci-numbers

Tom Locker said...

Facebook is censoring information about Benford’s Law and the Biden vote totals.
https://gnews.org/534248/

Windy Wilson said...

Biden suggests a 220 year old law that's never been used to try to impeach Trump with.
Biden gets tripped up by a law of statistics, a field the Democrat operatives have less than a college survey course understanding of.

From your lips to God's ear, although I suspect the true believers in the monstrosity of Trump would not be convinced even if Biden got on TV and instead of just saying he had the most extensive election fraud network in American History, he thanked the operatives in Michigan, Pennsylvania and New York who gave him the victory.