On the Combination Procedure of Correlated Errors

TL;DR

This paper presents a transparent, general method for combining correlated errors from multiple experimental measurements, explicitly separating statistical and systematic components, applicable to Gaussian and other error distributions.

Contribution

It introduces a new procedure to accurately decompose combined errors into statistical and systematic parts, accounting for correlations and extending to various error distributions.

Findings

Derived a general formula for Gaussian errors with correlations.

Defined disparity and misalignment angles for two measurements.

Provided a practical method for error component separation.

Abstract

When averages of different experimental determinations of the same quantity are computed, each with statistical and systematic error components, then frequently the statistical and systematic components of the combined error are quoted explicitly. These are important pieces of information since statistical errors scale differently and often more favorably with the sample size than most systematical or theoretical errors. In this communication we describe a transparent procedure by which the statistical and systematic error components of the combination uncertainty can be obtained. We develop a general method and derive a general formula for the case of Gaussian errors with or without correlations. The method can easily be applied to other error distributions, as well. For the case of two measurements, we also define disparity and misalignment angles, and discuss their relation to the combination weight factors.