Theory of random measurement errors: concepts, uses, and misuses

We present an overview of the theory of random measurement errors, focusing on the underlying concepts rather than on a strict mathematical formulation. Although the related literature is extensive, one can frequently encounter partly or completely wrong usages of the theory. In many cases, these mi...

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Main Authors: Zauner Branimir, Petrinec Branko, Bituh Tomislav, Ceci Saša, Volarić Nikola, Včev Aleksandar, Vukoja Andrea, Babić Dinko
Format: Article
Language:English
Published: Sciendo 2025-06-01
Series:Arhiv za Higijenu Rada i Toksikologiju
Subjects:
Online Access:https://doi.org/10.2478/aiht-2025-76-3977
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author Zauner Branimir
Petrinec Branko
Bituh Tomislav
Ceci Saša
Volarić Nikola
Včev Aleksandar
Vukoja Andrea
Babić Dinko
author_facet Zauner Branimir
Petrinec Branko
Bituh Tomislav
Ceci Saša
Volarić Nikola
Včev Aleksandar
Vukoja Andrea
Babić Dinko
author_sort Zauner Branimir
collection DOAJ
description We present an overview of the theory of random measurement errors, focusing on the underlying concepts rather than on a strict mathematical formulation. Although the related literature is extensive, one can frequently encounter partly or completely wrong usages of the theory. In many cases, these misuses stem from incomplete understanding of the basic principles. Our presentation is based on a discussion on similarities and differences between this theory and statistics, as they are used differently in analysing the results of an experiment. In statistics, the central parameters are the mean and standard deviation, which are related to a given statistical distribution. In the theory of random measurement errors, the mean has a different meaning, representing the best estimate of the true value of a measured quantity. The second parameter of importance is not standard deviation but the uncertainty of the mean, which sets the probability that the true value lies in a given interval around the mean. These conceptual differences are seldom pointed out, which sometimes results in doubtful or wrong analyses and presentations of measurement results. We illustrate our theoretical considerations with examples of proper and improper use of the theory.
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institution Kabale University
issn 1848-6312
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series Arhiv za Higijenu Rada i Toksikologiju
spelling doaj-art-cbd6c9520b704d61b8023325ea2105ea2025-08-20T03:29:53ZengSciendoArhiv za Higijenu Rada i Toksikologiju1848-63122025-06-01762798610.2478/aiht-2025-76-3977Theory of random measurement errors: concepts, uses, and misusesZauner Branimir0Petrinec Branko1Bituh Tomislav2Ceci Saša3Volarić Nikola4Včev Aleksandar5Vukoja Andrea6Babić Dinko7Institute for Medical Research and Occupational Health, Zagreb, CroatiaInstitute for Medical Research and Occupational Health, Zagreb, CroatiaInstitute for Medical Research and Occupational Health, Zagreb, CroatiaRuđer Bošković Institute, Zagreb, CroatiaJosip Juraj Strossmayer University of Osijek Faculty of Dental Medicine and Health, Osijek, CroatiaJosip Juraj Strossmayer University of Osijek Faculty of Dental Medicine and Health, Osijek, CroatiaJosip Juraj Strossmayer University of Osijek Faculty of Dental Medicine and Health, Osijek, CroatiaInstitute for Medical Research and Occupational Health, Zagreb, CroatiaWe present an overview of the theory of random measurement errors, focusing on the underlying concepts rather than on a strict mathematical formulation. Although the related literature is extensive, one can frequently encounter partly or completely wrong usages of the theory. In many cases, these misuses stem from incomplete understanding of the basic principles. Our presentation is based on a discussion on similarities and differences between this theory and statistics, as they are used differently in analysing the results of an experiment. In statistics, the central parameters are the mean and standard deviation, which are related to a given statistical distribution. In the theory of random measurement errors, the mean has a different meaning, representing the best estimate of the true value of a measured quantity. The second parameter of importance is not standard deviation but the uncertainty of the mean, which sets the probability that the true value lies in a given interval around the mean. These conceptual differences are seldom pointed out, which sometimes results in doubtful or wrong analyses and presentations of measurement results. We illustrate our theoretical considerations with examples of proper and improper use of the theory.https://doi.org/10.2478/aiht-2025-76-3977mean valuerelative uncertaintystatisticsuncertainty of the meannepouzdanost srednje vrijednostirelativna nepouzdanostsrednja vrijednoststatistika
spellingShingle Zauner Branimir
Petrinec Branko
Bituh Tomislav
Ceci Saša
Volarić Nikola
Včev Aleksandar
Vukoja Andrea
Babić Dinko
Theory of random measurement errors: concepts, uses, and misuses
Arhiv za Higijenu Rada i Toksikologiju
mean value
relative uncertainty
statistics
uncertainty of the mean
nepouzdanost srednje vrijednosti
relativna nepouzdanost
srednja vrijednost
statistika
title Theory of random measurement errors: concepts, uses, and misuses
title_full Theory of random measurement errors: concepts, uses, and misuses
title_fullStr Theory of random measurement errors: concepts, uses, and misuses
title_full_unstemmed Theory of random measurement errors: concepts, uses, and misuses
title_short Theory of random measurement errors: concepts, uses, and misuses
title_sort theory of random measurement errors concepts uses and misuses
topic mean value
relative uncertainty
statistics
uncertainty of the mean
nepouzdanost srednje vrijednosti
relativna nepouzdanost
srednja vrijednost
statistika
url https://doi.org/10.2478/aiht-2025-76-3977
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