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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| Format: | Article |
| Language: | English |
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Sciendo
2025-06-01
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| Series: | Arhiv za Higijenu Rada i Toksikologiju |
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| 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. |
| format | Article |
| id | doaj-art-cbd6c9520b704d61b8023325ea2105ea |
| institution | Kabale University |
| issn | 1848-6312 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Sciendo |
| record_format | Article |
| 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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