Correlation between repeated measurements: bane and boon of the GUM approach to the uncertainty of measurement

With measurement uncertainty estimation accounting for all relevant uncertainty contributions, the results of measurements using the same procedure on different objects or samples may no longer be considered as being independent, and correlations have to be taken into account. For this purpose, a simple approximation for the estimation of covariances is derived and applied to the estimation of uncertainty for some basic combinations of two measurement results. This covariance estimate is also applied to the estimation of uncertainty for the mean value of the results of replicate measurements on the same object or sample.

New tools: Uncertainty-based data evaluation

 The principles of uncertainty-based data evaluation are explained. Based on a brief review of recent publications on the topic, examples for application to standard procedures in analytical chemistry – calibration, method validation, standard addition etc., – are given. The performance and the advantages of uncertainty-based data evaluation are discussed. Received: 4 July 1998 · Accepted: 6 July 1998     

Shall we consider covariances?

 The impact of correlation between the reference points used in determination of a functional relationship by application of least-squares techniques is discussed. Calculations are based on an improved effective-variance approach to the general least-squares problem. From a simulation study, general conclusions about the impact of correlation are drawn. Standard addition as an example of a method using correlated data is discussed in detail. Received: 29 October 1997 · Accepted: 26 November 1997