Premium
Quantifying the Random Component of Measurement Error of Nominal Measurements Without a Gold Standard
Author(s) -
Akkerhuis T. S.,
de Mast J.
Publication year - 2016
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.2023
Subject(s) - component (thermodynamics) , observational error , estimator , outcome (game theory) , random error , statistics , range (aeronautics) , gold standard (test) , random effects model , standard error , nominal level , computer science , mathematics , algorithm , engineering , physics , thermodynamics , medicine , confidence interval , meta analysis , mathematical economics , aerospace engineering
It is well known that measurement error of numerical measurements can be divided into a systematic and a random component and that only the latter component is estimable if there is no gold standard or reference standard available. In this paper, we consider measurement error of nominal measurements. We motivate that, on a nominal measurement scale too, measurement error has a systematic and a random component and only the random component is estimable without gold standard. Especially in literature about binary measurement error, it is common to quantify measurement error by ‘false classification probabilities’: the probabilities that measurement outcomes are unequal to the correct outcomes. These probabilities can be split up in a systematic and a random component. We quantify the random component by ‘inconsistent classification probabilities’ ( ICP s): the probabilities that a measurement outcome is unequal to the modal (instead of correct) outcome. Systematic measurement error then is the event that this modal outcome is unequal to the correct outcome. We introduce an estimator for the ICP s and evaluate its properties in a simulation study. We end with a case study that demonstrates not only the determination and use of the ICP s but also demonstrates how the proposed modeling can be used for formal hypothesis testing. Things to test include differences between appraisers and random classification by a single appraiser. Copyright © 2016 John Wiley & Sons, Ltd.