Compositional analysis statistical uncertainty

Consider a binary alloy. Because of the statistical nature of single atom counting, the statistical uncertainty in the compositional analysis is given by... 

NNs over the entire range of film compositions investigated. This preference is partially reversed for a distance of 2 NN, where a small local maximum is visible for the surface with 25% Pd, indicating a preference for Pd atoms separated by 2 NN units, as they are present in the (2 x 2) structure on the (111) plane of ordered CujPd bulk alloys. In an SRO analysis, such a (2 x 2) structure would generate values of a(2) = l and 0 (r) = —1/3 for r 2. In the STM-based data, however, the variations of a(r) are much less enhanced, and for r>2, they lie within the margins of the statistical uncertainty. Even prolonged anneahng at lower T was shown to not yield any periodic superstmcture [57]. Chapter 11 will include a thermodynamic description of the lateral atom distribution, and it wiU show why ordered structures are experimentally inaccessible to most surface alloys. 

Results from the analysis of the RM and the certified value and their uncertainties are compared using simple statistical tests (Ihnat 1993,1998a). If the measured concentration value agrees with the certified value, the analyst can deduce with some confidence that the method is applicable to the analysis of materials of similar composition. If there is disagreement, the method as applied exhibits a bias and underlying causes of error should be sought and corrected, or their effects minimized. 

It is notable that such kinds of error sources are fairly treated using the concept of measurement uncertainty which makes no difference between random and systematic . When simulated samples with known analyte content can be prepared, the effect of the matrix is a matter of direct investigation in respect of its chemical composition as well as physical properties that influence the result and may be at different levels for analytical samples and a calibration standard. It has long since been suggested in examination of matrix effects [26, 27] that the influence of matrix factors be varied (at least) at two levels corresponding to their upper and lower limits in accordance with an appropriate experimental design. The results from such an experiment enable the main effects of the factors and also interaction effects to be estimated as coefficients in a polynomial regression model, with the variance of matrix-induced error found by statistical analysis. This variance is simply the (squared) standard uncertainty we seek for the matrix effects. 

Saisana M., Saltelli A., Tarantola S., (2005). Uncertainty and Sensitivity analysis techniques as tools for the quality assessment of composite indicators. Journal of the Royal Statistical Society A, 168, (2), pp. 1-17. 

The statistical analysis of individual olfactograms generated by a large panel has shown an optimal composition of between six and ten members for routine analyses with a NIF uncertainty of 20% and 5%, respectively (14). 

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