Comparing Different Uncertainty Measures to Quantify Measurement Uncertainties in High School Science Experiments

TL;DR

This paper compares various uncertainty measures for high school science data, evaluating their mathematical complexity and statistical reliability to aid students in understanding measurement variation.

Contribution

It introduces a sequence of uncertainty measures with increasing complexity and quality, tailored for different educational levels.

Findings

Higher mathematical complexity correlates with better statistical quality

A proposed sequence of uncertainty measures suits various educational levels

Monte Carlo simulations validate the effectiveness of alternative measures

Abstract

Interpreting experimental data in high school experiments can be a difficult task for students, especially when there is large variation in the data. At the same time, calculating the standard deviation poses a challenge for students. In this article, we look at alternative uncertainty measures to describe the variation in data sets. A comparison is done in terms of mathematical complexity and statistical quality. The determination of mathematical complexity is based on different mathematics curricula. The statistical quality is determined using a Monte Carlo simulation in which these uncertainty measures are compared to the standard deviation. Results indicate that an increase in complexity goes hand in hand with quality. Additionally, we propose a sequence of these uncertainty measures with increasing mathematical complexity and increasing quality. As such, this work provides a theoretical background to implement uncertainty measures suitable for different educational levels.