Statistical calibration

In the following, the stages of the analytical process will be dealt with in some detail, viz. sampling principles, sample preparation, principles of analytical measurement, and analytical evaluation. Because of their significance, the stages signal generation, calibration, statistical evaluation, and data interpretation will be treated in separate chapters. 

Because of the way the data was created, we can rely on the calibration statistics as an indicator of performance. There is no need to use a validation set of data here. Validation sets are required mainly to assess the effects of noise and intercorrelation. Our simulated data contains no noise. Furthermore, since we are using only one wavelength or one factor, intercorrelation effects are not operative, and can be ignored. Therefore the final test lies in the values obtained from the sets of calibration results, which are presented in Table 27-1. 

Those results seem to bear out our conjecture. The different calibration statistics all show the same effects the full-wavelength approach does seem to be sort of split the difference and accommodate some, but not all, of the non-linearities the algorithm... 

Table 27-1 Calibration statistics obtained from the three calibration models discussed in the text...

We will not repeat Anscombe s presentation, but we will describe what he did, and strongly recommend that the original paper be obtained and perused (or alternatively, the paper by Fearn [15]). In his classic paper, Anscombe provides four sets of (synthetic, to be sure) univariate data, with obviously different characteristics. The data are arranged so as to permit univariate regression to be applied to each set. The defining characteristic of one of the sets is severe nonlinearity. But when you do the regression calculations, all four sets of data are found to have identical calibration statistics the slope, y-intercept, SEE, R2, F-test and residual sum of squares are the same for all four sets of data. Since the numeric values that are calculated are the same for all data sets, it is clearly impossible to use these numeric values to identify any of the characteristics that make each set unique. In the case that is of interest to us, those statistics provide no clue as to the presence or absence of nonlinearity. 

Statistics have been used in chemical analysis in increasing amounts to quantify errors. The focus shifts now to other areas, such as in sampling and in measurement calibrations. Statistical and computer methods can be brought into use to give a quantified amount of error and to clarify complex mixture problems. These areas are a part of chemometrics as we use the term today. 

Table 5.4.1 Calibration statistics of faecal bile acids (Bas reprinted from [16]). CA Cholic acid, CDCA chenodeoxycholic acid, DCA deoxycholic acid, LCA lithocholic acid ... 

In principle, all performance measures of an analytical procedure mentioned in the title of this section can be derived from a certain critical signal value, ycrit. These performance measures are of special interest in trace analysis. The approaches to estimation of these measures may be subdivided into methods of blank statistics , which use only blank measurement statistics, and methods of calibration statistics , which in addition take into account calibration confidence band statistics. 

States National Bureau of Standards Calibration Statistics (NBS), later the National Institute of Standards and Technology (NIST), introduced a measurement quality control concept called measurement assurance, and developed measurement assurance programs, or MAPs, for high-level calibration processes. 

Table III. Calibration statistics for all wine color measures.

Table 2 NIRS calibration statistics for com silage used at the University of Wisconsin for broad-based prediction equations used to estimate neutral detergent fiber (NDF), in vitro trae digestibility (IVTD), protein, and starch of com silage.

Atomic methods also benefit from the incorporation of microcomputers into the instruments. Figure 10.7 shows the scheme of an atomic absorption spectrometer with a built-in microprocessor which controls the signal from the detector, previously amplified and converted to digital form. A series of ROMs store the programs for zero-setting, calibration, statistical treatment and calculation of integration areas and times. The microprocessor modulates the... 

Nufiez-Sanchez et al. (37) evaluated NIR calibration equations for the main constituents of ewe s cheese under two different sample preparation methods (homogenized and intact) and under reflectance and fiber-optic probe. The SECV values obtained for the homogenized cheeses and for both analysis modes were comparable for fat, protein, and dry matter. The calibration statistics for the intact cheese analyzed by fiber-optic probe were higher than those obtained with homogenized cheese. 

D Will show apparent improvement on calibration statistics could result in overfit of the calibration data... 

Calibration Statistics for Predicting the MBM Percentage of Ground and Intact Compound Feeds... 

A similar experiment has also been carried out with bread dough, and the calibration statistics are given in Table 19.3. This application was accomplished with a 19-filter instrument, and as for biscuit doughs the results indicate that NIR could be used to screen for gross errors in ingredient levels. 

The two instrumental techniques are compared in Table 24.1 on the basis of their calibration statistics and the standard error of performance (SEP) with a confirmation set. NIR would appear to have an edge over FT/IR on all counts correlation is better, equations are more robust (higher F values), and there are lower errors. If one adds to this comparison two time factors, NIR emerges as a clear winner, as is shown in Table 24.1. 

The RBF kernel (experiments 16-24), with ACp between 0.96 and 0.97, has better calibration statistics than the linear kernel, but its performance in prediction only equals that of the linear SVM. Although many tests were performed for the neural kernel (experiments 25-51), the prediction statistics are low, with ACp between 0.64 and 0.88. This result is surprising, because the tanh function gives very good results in neural networks. Even the training statistics are low for the neural kernel, with AC, between 0.68 and 0.89... 

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