Sample Scored Problem

Mirex levels in the blood of pregnant women in Jackson, Mississippi, and the Mississippi Delta area where mirex was extensively used were correlated with the health of the infants they bore. The mean mirex level in maternal blood was 0.54 pg/L (ppb) for 106 samples however, mirex levels in the blood of the infants were not correlated with differences in gestation times, Apgar score, or other problems at birth. Only three children with neurological problems had mothers with pesticide levels, including mirex, above the mean levels (Lloyd et al. 1974). 

As in many such problems, some form of pretreatment of the data is warranted. In all applications discussed here, the analytical data either have been untreated or have been normalized to relative concentration of each peak in the sample. Quality Assurance. Principal components analysis can be used to detect large sample differences that may be due to instrument error, noise, etc. This is illustrated by using samples 17-20 in Appendix I (Figure 6). These samples are replicate assays of a 1 1 1 1 mixture of the standard Aroclors. Fitting these data for the four samples to a 2-component model and plotting the two first principal components (Theta 1 and Theta 2 [scores] in... 

Classification To illustrate the use of SIMCA in classification problems, we applied the method to the data for 23 samples of Aroclors and their mixtures (samples 1-23 in Appendix I). In this example, the Aroclor content of the three samples of transformer oil was unknown. Samples 1-4, 5-8, 9-12 and 13-16, were Aroclors 1242, 1248, 1254, and 1260, respectively. Samples 17-20 were 1 1 1 1 mixtures of the Aroclors. Application of SIMCA to these data generated a principal components score plot (Figure 12) that shows the transformer oil is similar, but not... 

HCA is a common tool that is used to determine the natural grouping of objects, based on their multivariate responses [75]. In PAT, this method can be used to determine natural groupings of samples or variables in a data set. Like the classification methods discussed above, HCA requires the specification of a space and a distance measure. However, unlike those methods, HCA does not involve the development of a classification rule, but rather a linkage rule, as discussed below. For a given problem, the selection of the space (e.g., original x variable space, PC score space) and distance measure (e.g.. Euclidean, Mahalanobis) depends on the specific information that the user wants to extract. For example, for a spectral data set, one can choose PC score space with Mahalanobis distance measure to better reflect separation that originates from both strong and weak spectral effects. 

Scores Plot (Sa nple Diagnostic) The score plots show the relationship of the samples in LS row space and are examined for consistency with what is known about dse data set. Look for unusual or inconsistent patterns which can indicate potential problems with the model and/or samples (see also PCA, Section 4.2.2). 1b the PCA discussion the scores are referred to as PCs, but in PLS they are referred to as factors. 

The complete design is seen in the score space with replicate center points clearly visible. Note that the interpretation of scores plots is not always as straightforward as in this example. The experimental design is not seen if the experiment is not well designed or if the problem is high dimensional. The level of impEcidy modeled components (e.g., component O also has an effect on the relative position of the samples in score space. For this example, the effect of C on the relative placement of the samples in score space is small. 

One way to resolve these inconsistencies is to plot liie spectra of samples 3 and 11 and compare the differences in the raw data. Figure 5.99a displays the two spectra and the difference spectrum. The ttv O spectra are the same except for slight differences which can be attributed to measurement noise. Sample 3 is known to be the problem given the known concentrations and the spatial relationsliip between the other samples in the scores plots (i.e., it should be in the lower center portion of the graph). This means that either sample 3 was incorrectly prepared to have the same concentration as sample II, or sample 11 was measured when sample 3 was thought to have been measured. When the spectrum of sample 3 is remeasured, the resulting spectrum is very different from sample 11 (see Figure 5.99b). 

A significant source of false-negative scores stems from DNA samples containing impurities that inhibit PCR amplification. Such samples are readily detected by noting the relative intensities of PCR products in an RAPD pattern other than the particular polymorphism being scored (Fig. 4, lane 9). If bands that are monomorphic throughout a population are weak or absent in an individual sample, it is likely that this sample contains some inhibitory contaminant. Further purification of the sample by any of a number of standard protocols normally corrects this problem. 

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