Both of the standardization methods appear to work well with factor analysis routines. Standardization methods should be tested and adjusted, if necessary, after a cross-correlation test of the calibration spectra. This test involves using each calibration standard, in turn, as an unknown and the others as the learning set, and then calculating the standard error of prediction.^18,19
In the following two examples, quantitative analyses are performed in one case with and in the other without standardization of spectra.

1. Vinyl acetate concentration in polyethylene copolymer pellets

Vinyl acetate concentrations in pellets of varying sizes are determined by FTIR-PAS and a PLS factor analysis routine (Spectra-Calc, Galactic Industries Corp., Salem, NH, USA) without sample preparation. The direct analysis of pellets is complicated by variations in sample volume and morphology. This variability and the other potential changes listed above are accounted for by using the area under the C-H band (2750-3120 cm^-1)for standardization of spectra. The analysis conditions are given in Table 4. A cross- correlation analysis of the standards set resulted in a SEP value of 0.55% (mass). The reproducibility of the PLS analysis was tested by twice running spectra on pellets of three concentrations. The second run involved reloading the same pellets in the sample cup followed by the purge and seal operation, and spectrum acquisition. The average values of the vinyl acetate concentrations were 5.89%, 9.49%, and 16.27% and the differences between the two analysis values for each concentration were 0.12%, 0.21%, and 0.00%, respectively. The manufacturer's stated concentrations for the samples were 5.84%, 9.36%, and 14.90%. All of the data are consistent with the cross-correlation analysis SEP except for the highest concentration value reported by the manufacturer.
Figure 21 shows typical FTIR-PAS spectra of two vinyl acetate-polyethylene copolymer samples that were in the learning set. The cross-correlation analysis results are plotted in Fig. 22.

2. Ash concentration in coal

In industry, coal is cleaned by various processes in order to reduce the concentration of ash which causes boiler fouling and environmental problems. The froth flotation cleaning process produces float material with reduced ash concentration and a sink material with high ash content. FTIR-PAS can be used to rapidly check the ash concentration in a coal cleaning operation using standards that are synthesized from float and sink material. The analysis conditions are given in Table 4. The coal samples were in fine powder form and were formulated to have different ash concentrations by mixing calculated weights of float and sink material. Portions of the mixtures were measured out for FTIR-PAS analysis by volume simply by filling small stainless steel sample cups as shown in Fig. 5 and sliding a spatula across the cup rim to remove excess powder. Fig. 23 shows two typical spectra of the float (6% ash) and sink (31.6% ash) material that were used in the analyses. The results of the cross-correlation analysis are plotted in Fig. 24. A SEP of 0.44% (mass) was obtained.