Quantifying and handling errors in instrumental measurements using the measurement error theory

Abstract

AbstractMeasurement error modelling is used for investigating the influence of measurement/sampling error on univariate predictions of water content and water‐holding capacity (reference measurement) from nuclear magnetic resonance (NMR) relaxations (instrumental) measured on two gadoid fish species. This is a new way of using the measurement error theory. Reliability ratios illustrate that the models for the two fish species are influenced differently by the error. However, the error seems to influence the predictions of the two reference measures in the same way. The effect of using replicated x‐measurements is illustrated by simulated data and by NMR relaxations measured several times on each fish. The standard error of the physical determination of the reference values is lower than the standard error of the NMR measurements. In this case, lower prediction error is obtained by replicating the instrumental measurements. A new general formula is given for how to correct the least squares regression coefficient when a different number of replicated x‐measurements is used for prediction than for calibration. It is shown that the correction should be applied when the number of replicates in prediction is less than the number in calibration. This can be relevant for on‐line applications and in other situations where it is important to make fast measurements in the prediction phase. Copyright © 2004 John Wiley & Sons, Ltd.