Uncertainty in Measurement: Procedures for Determining Uncertainty With Application to Clinical Laboratory Calculations

Frenkel, Robert B., Farrance, Ian, Robert B. Frenkel, Ian Farrance

In Part II of this review we consider the very common case of multiple inputs to a measurement process. We derive, using only elementary steps and the basic mathematics covered in Part I, the formula for the propagation of uncertainties from the inputs to the output. The Gaussian density distribution is briefly explained, since an understanding of this distribution is needed for the determination of so-called expanded uncertainties at the end of a measurement process. The propagation formula in general involves correlations among the inputs, although in many cases these correlations can be considered negligible. Correlations, however, need to be taken into account in related matters such as line-fitting and have particular relevance to method comparisons. These topics are addressed briefly. We next discuss the important question of bias and its incorporation into the expression of uncertainty. We present, finally, six real-world cases in clinical chemistry where uncertainty in the estimated value of the measurand is calculated using the propagation formula.