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Title: Two Theories Of Experimental Error
Author: A. R. Colclough
Source: 1986 Measurement Science Conference
Year Published: 1986
Abstract: Following recent international recommendations o n the combination of experimental uncertainties. two theories of error are identified and their possible justlflcations assessed. They are the orthodox theory based on the familiar distinction between random and systematic errors and the randomatlc theory which dispenses with the distl.nctlon and assigns standard deviations to ail errors. treating them as the orthodox theory treats random errors. The orthodox theory suffers from a number of important confusions about the nature of its central distlnctlon. about the combination of uncertainties and about which populations of results can correctly be said to contain random errors. These confusions are clarified and the central distinction is argued to be objective and Indispensibie. Three arguments are developed for the randomatic theory: (1) that it is implied by the generally accepted law of error propagation. (ii) that all so-called systematic errors belong to popuiatlons characterised by hitherto unnoticed frequency-based dlstributlons. and (Iii) that they belong to subjectlvist p r i o r distributions. But. upon examination. the argument in terms of the law of error propagatlon is found to beg key controversial questions. the frequency-based * distributions are found not always to be unique or of suitable form and the subjectivist distributions are found to be unreailstlc. Thus the randomatlc theory remains unjustified by objective standards. Moreover. its use could lead to the underestlmatlon of uncertalntles. New recommendations are formulated which are orthodox in general character.




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