Lotka's Inverse Square Law of Scientific Productivity: Its Methods and Statistics

TL;DR

This paper critically examines Lotka's original derivation of his inverse square law of scientific productivity, revealing methodological flaws and its influence on current practices in identifying power-law distributions.

Contribution

It demonstrates that Lotka's data truncation violated modern statistical norms and shows his role in popularizing the R^2 log-log regression method for power-law detection.

Findings

Lotka's data truncation was inconsistent with modern statistical standards.

Lotka's use of R^2 on log-log plots influenced current power-law identification.

The paper clarifies the historical and methodological context of Lotka's law.

Abstract

This brief communication analyzes the statistics and methods Lotka used to derive his inverse square law of scientific productivity from the standpoint of modern theory. It finds that he violated the norms of this theory by extremely truncating his data on the right. It also proves that Lotka himself played an important role in establishing the commonly used method of identifying power-law behavior by the R^2 fit to a regression line on a log-log plot that modern theory considers unreliable by basing the derivation of his law on this very method.