Comparison of recent estimators of uncertainty on the mean for small measurement samples with normal and non-normal error distributions

TL;DR

This paper reviews recent methods for estimating uncertainty in the mean of small measurement samples, comparing their effectiveness across normal and non-normal error distributions using synthetic data.

Contribution

It provides a comparative analysis of recent estimators for measurement uncertainty, highlighting their performance differences under various error distribution conditions.

Findings

Certain estimators outperform traditional methods with non-normal errors.

Performance varies significantly depending on the error distribution.

Some recent proposals offer more accurate uncertainty estimates for small samples.

Abstract

We review the alternative proposals introduced recently in the literature to update the standard formula to estimate the uncertainty on the mean of repeated measurements, and we compare their performances on synthetic examples with normal and non-normal error distributions.