On two methods to evaluate the uncertainty of derivatives calculated from polynomials fitted to experimental data

Abstract

We compare the performance of two procedures used for the evaluation of uncertainty of derivatives computed from a polynomial fitted to experimental data. These procedures agree with international recommendations and they are valid independently of the experimental technique used to obtain the data. The first procedure involves performing a least-squares polynomial adjustment under uncertainty. The second procedure is based on Monte Carlo techniques. Both are computer-assisted. As an example, we evaluated the standard uncertainty associated with the gradient of a surface fitted to experimental data that formed a set of points in a three-dimensional space. We found that both methods render very similar results. © 2005 BIPM and IOP Publishing Ltd.