Interpretation of Calibration Evaluation: I. Graphical Aspects

Abstract

Introduction T he legendary sculptor Michelangelo noted in his diaries that he could visualise statues, including his exquisite statue of David, inside the blocks of stone and that all he had to do was to bring them out. A NIR spectrum can be considered in much the same way. All the information relating to the sample is contained in the spectrum. What we as operators have to do is to use the right mathematical measures to translate the spectral data into the information we need. Modern NIR software contains many options, the chisels that can help us bring the statue out of the stone. This article is included mainly for the benefit of those who want to learn more about NIR technology than just its application. Interpretation of calibration evaluation means finding out why the calibration worked or why it did not work. The first step in calibration evaluation is to look at the appropriate statistics. The r, bias and RPD figures are the simplest way of evaluating a calibration model quickly. The first step in interpretation of a NIR exercise is look at the data, both spectral and reference. This can be done as the data are being generated during daily analysis, or while recording spectra for development of calibration models. In this way the operator will become familiar with what the data should look like, and also the shapes of the spectra. At this time, the outlier may rear its ugly head. An outlier is a sample that does not conform to the rest of the population. There are two main types of outlier. The first type is the spectral outlier which can be detected before any attempts are made at calibration. The other type is a prediction outlier which involves the reference data. Figures 1 and 2 show typical spectral outliers. The insets show an expanded view of the five spectra recorded for each sample together with the associated prediction results. In the first case, the outlier caused the predicted result to be low, while in the second example the predicted result was higher than results predicted for the other four spectra. Outliers can be detected and corrective measures taken at the time of calibration development and validation. Most NIR software includes options for their detection although there are no hard and fast rules about what exactly constitutes an outlier. Some definitions are based on the spectral data alone, others on the results of prediction. In the case of spectral data, the consensus appears to be that an outlier is a sample/spectrum that differs from the mean of the corresponding population by three or more Mahalanobis distances. Oversimplified, the Mahalanobis distance is the distance of the spectral data for an individual sample from that of the population mean at each wavelength point. In the case of prediction results, an outlier is defined as a sample that generates a residual that differs from the mean of the residuals by three or more times the SEP. The most important first step to take when an outlier has been indicated is to verify that it is indeed an outlier. First, check that all reference data have been correctly entered and that all sample identification is correct. The next steps can best be done by re-scanning the sample in the instrument and re-testing it by the appropriate reference method. Re-testing by the reference method may result in a significant change in the data. If this happens the sample has to be re-tested again, to determine which of the first two results is the correct one. This Interpretation of Calibration Evaluation: I. Graphical Aspects