How to Combine Independent Data Sets for the Same Quantity

TL;DR

This paper introduces conflation, a mathematical method for combining independent experimental data measuring the same quantity, optimizing information retention and providing transparent, practical applications in physics measurements.

Contribution

The paper presents a new, easy-to-calculate method called conflation for consolidating independent data sets, with detailed properties and applications to normal data and physical constants.

Findings

Conflation minimizes Shannon information loss when combining data.

The method is visualizable and computationally straightforward.

Applications include measurements of fundamental constants and high energy physics data.

Abstract

This paper describes a recent mathematical method called conflation for consolidating data from independent experiments that are designed to measure the same quantity, such as Planck's constant or the mass of the top quark. Conflation is easy to calculate and visualize, and minimizes the maximum loss in Shannon information in consolidating several independent distributions into a single distribution. In order to benefit the experimentalist with a much more transparent presentation than the previous mathematical treatise, the main basic properties of conflation are derived in the special case of normal (Gaussian) data. Included are examples of applications to real data from measurements of the fundamental physical constants and from measurements in high energy physics, and the conflation operation is generalized to weighted conflation for situations when the underlying experiments are not uniformly reliable.