Asymmetric Systematic Errors

TL;DR

This paper addresses the improper traditional methods of combining asymmetric systematic errors, proposing consistent techniques for their combination, evaluation of chi-squared, and forming weighted sums, improving accuracy in error analysis.

Contribution

It introduces justified methods for combining asymmetric systematic errors, replacing the traditional but flawed quadrature approach, and provides techniques for chi-squared evaluation and weighted sums.

Findings

Traditional quadrature method is often inappropriate.

Proposed consistent techniques improve error combination accuracy.

Enhanced methods for chi-squared evaluation and weighted sums.

Abstract

Asymmetric systematic errors arise when there is a non-linear dependence of a result on a nuisance parameter. Their combination is traditionally done by adding positive and negative deviations separately in quadrature. There is no sound justification for this, and it is shown that indeed it is sometimes clearly inappropriate. Consistent techniques are given for this combination of errors, and also for evaluating $\chi^2$, and for forming weighted sums.