Review article

https://doi.org/10.2478/aiht-2025-76-3977

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

Branimir Zauner ; Institute for Medical Research and Occupational Health, Zagreb, Croatia
Branko Petrinec ; Institute for Medical Research and Occupational Health, Josip Juraj Strossmayer University of Osijek Faculty of Dental Medicine and Health, Osijek, CroatiaZagreb, Croatia,
Tomislav Bituh ; Institute for Medical Research and Occupational Health, Zagreb, Croatia
Saša Ceci ; Ruđer Bošković Institute, Zagreb, Croatia
Nikola Volarić ; Josip Juraj Strossmayer University of Osijek Faculty of Dental Medicine and Health, Osijek, Croatia
Aleksandar Včev ; Josip Juraj Strossmayer University of Osijek Faculty of Dental Medicine and Health, Osijek, Croatia
Andrea Vukoja ; Josip Juraj Strossmayer University of Osijek Faculty of Dental Medicine and Health, Osijek, Croatia 4 University Hospital Centre Osijek, Croatia
Dinko Babić ; Institute for Medical Research and Occupational Health, Zagreb, Croatia

Abstract

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.

Keywords

mean value; relative uncertainty; statistics; uncertainty of the mean

Hrčak ID:

332313

URI

https://hrcak.srce.hr/332313

Publication date:

17.6.2025.

Article data in other languages: croatian

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