Sample presentation error

Equation (4.20) was proposed by Hoskuldsson [65] many years ago and has been adopted by the American Society for Testing and Materials (ASTM) [59]. It generalises the univariate expression to the multivariate context and concisely describes the error propagated from three uncertainty sources to the standard error of the predicted concentration calibration concentration errors, errors in calibration instrumental signals and errors in test sample signals. Equations (4.19) and (4.20) assume that calibrations standards are representative of the test or future samples. However, if the test or future (real) sample presents uncalibrated components or spectral artefacts, the residuals will be abnormally large. In this case, the sample should be classified as an outlier and the analyte concentration cannot be predicted by the current model. This constitutes the basis of the excellent outlier detection capabilities of first-order multivariate methodologies. 

Frustratingly, we cannot calculate exactly how much sampling error will be present in any individual sample. The error is random in nature and with any given sample we may over or underestimate the true situation, or (if it was an unusually lucky sample) we might be almost bang on. What we can estimate is a typical amount of sampling... 

Randomization is done to minimize the effects of uncontrolled sources of variation or error and to eliminate bias. It involves ordering sample treatments in such a way that each treatment has an equal chance of being selected. In sensory testing, the order of sample presentation to each panelist is randomized. 

So far, we considered the application of a liner least squares technique in the case when no systematic error has been present in the observed powder diffraction data. However, as we already know, in many cases the measured Bragg angles are affected by a systematic sample displacement or zero shift error. The first systematic error affects each data point differently and considering Eq. 3.4 (section 3.5.5), when a sample displacement error, s, is present in the data, Eq. 5.43 becomes... 

For highly luminescent samples, the error may be reduced by decreasing the time-window (the error is approximately 1% for a 20% window) (Schippers and Dekkers, 1981), or one might be justified in simply correcting the value to account for this known effect. Obviously, there are other sources of error in polarization measurements of this type. The PEM itself is not a perfect optical element, and other elements including linear polarizers, sample containers, filters, mirrors, etc. all lead to sources of error. One also needs to consider the statistical nature of these measurements as described below, and, as a result, lum values obtained with 50% time-windows are usually presented as obtained without correction. 

The techniques for removing representative samples from an equilibrium mixture are quite critical and are probably a major source of error in producing scattered and false data. Vapor sampling presented few problems. Since the equilibrium vapor was pumped directly through the sampling coil at both ends, a vapor sample was secured without affecting the temperature or pressure of the rest of the system. 

Errors from the NIR instrument including electronic noise, spectral noise, and variation in sample presentation. It is often difficult to get an estimate of this error. 

This source of error can be substantially reduced by performing an in-house audit for procedures, equipment, and personnel, paying particular attention to sample presentation, drying biases, and random moisture losses upon grinding [6]. 

Comments The repack error, sometimes referred to as the SDD or standard error of differences for replicate measurements (SED replicates), is calculated to allow accurate estimation of the variation in an analytical method due to both sampling and presentation errors. It is a measure of precision for an analytical method. 

There are four main sources of error associated with the sample. These are (a) the source of the sample, (b) the sampling method, (c) the sample itself, including sample preparation, and (d) final sample presentation. 

The monitoring of PAHs in enviromnental samples presents several problems. One of the main limitations is related with the low concentration levels of PAHs to be monitored in the samples, with the consequent difficulty for being detected and quantified. Another limitation is related with the inadvertent errors during the sampling. In addition to this, the complexity of the samples, the undoubtedly presence of interfering substances, and the necessity of accurate and fast analysis, do the monitoring of PAHs an analytical challenge. 

The magnitude of a method s relative error depends on how accurately the signal is measured, how accurately the value of k in equations 3.1 or 3.2 is known, and the ease of handling the sample without loss or contamination. In general, total analysis methods produce results of high accuracy, and concentration methods range from high to low accuracy. A more detailed discussion of accuracy is presented in Chapter 4. 

Significance tests, however, also are subject to type 2 errors in which the null hypothesis is falsely retained. Consider, for example, the situation shown in Figure 4.12b, where S is exactly equal to (Sa)dl. In this case the probability of a type 2 error is 50% since half of the signals arising from the sample s population fall below the detection limit. Thus, there is only a 50 50 probability that an analyte at the lUPAC detection limit will be detected. As defined, the lUPAC definition for the detection limit only indicates the smallest signal for which we can say, at a significance level of a, that an analyte is present in the sample. Failing to detect the analyte, however, does not imply that it is not present. 

Any acid-soluble materials present in the sample will react with HF or H2SO4. If the products of these reactions are volatile or decompose at the ignition temperature of 1200 °C, then the change in weight will not be due solely to the volatilization of SiF4. The result is a positive determinate error. 

Accuracy The accuracy of a gas chromatographic method varies substantially from sample to sample. For routine samples, accuracies of 1-5% are common. For analytes present at very low concentration levels, for samples with complex matrices, or for samples requiring significant processing before analysis, accuracy may be substantially poorer. In the analysis for trihalomethanes described in Method 12.1, for example, determinate errors as large as +25% are possible. ... 

A visual inspection of a two-sample chart provides an effective means for qualitatively evaluating the results obtained by each analyst and of the capabilities of a proposed standard method. If no random errors are present, then all points will be found on the 45° line. The length of a perpendicular line from any point to the 45° line, therefore, is proportional to the effect of random error on that analyst s results (Figure 14.18). The distance from the intersection of the lines for the mean values of samples X and Y, to the perpendicular projection of a point on the 45° line, is proportional to the analyst s systematic error (Figure 14.18). An ideal standard method is characterized by small random errors and small systematic errors due to the analysts and should show a compact clustering of points that is more circular than elliptical. 

The data used to construct a two-sample chart can also be used to separate the total variation of the data, Otot> into contributions from random error. Grand) and systematic errors due to the analysts, Osys. Since an analyst s systematic errors should be present at the same level in the analysis of samples X and Y, the difference, D, between the results for the two samples... 

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