Historical examples of frauds discovered because someone tried to mimic a uniform random sequence

Question

So, I'm preparing a talk about the well known fact that humans are bad at the task of generating uniformly random sequences of numbers when asked to do so.

I would like to spice the talk a bit by presenting some real cases where perhaps some tax fraud or bad science was revealed by a simple frequency analysis of the compromised data. For example a case were a scientist might have displaced some data points to better fit a specific conclusion and that it was discovered by analyzing the end digits of the values he manipulated. Or perhaps some person that changes a few small numbers here and there while working for a bank to get some money flowing to his account and then was discovered by another simple frequency analysis.

In short, I would like to know easy to explain examples of people been caught in some fraud because they though that they were able to emulate random numbers by themselves.

I asked this question in Cryptography-stack but it was closed and recommended to be moved here.

Thank you in advance.

Answer 1

A classical example is uncovering by Kolmogorov of the fraud in the work of a biologist Ermolaeva. This was the time when the Soviet authorities endorsed a pseudoscientific heredity theory of Lysenko, and the work of Ermolaeva was aimed at proving by statistical data that Mendel's heredity law is wrong.

The paper of Kolmogorov is called "On a new confirmation of Mendel's law", published in Doklady of the Academy of Scences, 27, 1 (1940) 38-42.

The full story is told in detail here (in Russian).