On computation of a common mean

TL;DR

This paper compares common methods for computing a shared mean from multiple measurements, introduces a new robust estimate, and evaluates their performance with simulated and real data.

Contribution

It proposes a new combined estimate to improve robustness and realism in calculating a common mean, addressing issues of existing methods.

Findings

The new method enhances robustness against measurement discrepancies.

Median and weighted average methods are compared using simulated and real data.

The proposed approach provides more reliable uncertainty estimates.

Abstract

Combining several independent measurements of the same physical quantity is one of the most important tasks in metrology. Small samples, biased input estimates, not always adequate reported uncertainties, and unknown error distribution make a rigorous solution very difficult, if not impossible. For this reason, many methods to compute a common mean and its uncertainty were proposed, each with own advantages and shortcomings. Most of them are variants of the weighted average (WA) approach with different strategies to compute WA and its standard deviation. Median estimate became also increasingly popular during recent years. In this paper, these two methods in most widely used modifications are compared using simulated and real data. To overcome some problems of known approaches to compute the WA uncertainty, a new combined estimate has been proposed. It has been shown that the proposed method can help to obtain more robust and realistic estimate suitable for both consistent and discrepant measurements.