Standard error of performance

The standard error of performance, also termed the standard error of prediction (SEP), which represents an estimate of the prediction error (1 sigma) for a regression line is given as ... 

Equation 59-11 indicates that the correlation coefficient is represented by the square root of one minus the ratio comprised of the square of the standard error of performance, to the square of the standard deviation of all X],... 

In a multivariate calibration, where a set of NIR spectra (Xnxk, N samples and K variables) is regressed onto a continuous variable (yivxi) such as the fat or moisture content, the statistical errors, the accuracy, are most often used as a quality measure of the calibration. The absolutely most common quality measure of a multivariate calibration is the prediction error, expressed either as root mean square error of prediction (RMSEP) or standard error of performance (SEP). Both are calculated and are the result of a validation process, such as test set or cross-validation. These prediction errors are defined as ... 

The intact approach has also been applied to cereal food products (6, 23), which encompass a very wide range of particle sizes and shapes from flour to flakes, puffed grains, extruded products, crackers, and flnes. A PLS regression model was developed to predict fat in intact cereal products. The model had a root mean squared standard error of performance of 11 g kg (range 1-205 g kg ) and coefficient of determination of 0.98 (23). When contrasted with models developed with similar products in a ground state, the latter had comparable standard errors of performance of 10-11 g kg fat and coefficients of determination of 0.98-0.99 (29,40,45). 

Comments The SEP is also termed the standard error of performance, also known as the standard deviation for the residuals due to differences between actual (primary wet chemical analytical values) and the NIR predicted values for samples outside of the calibration set using a specific calibration equation. 

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. 

Principal component analysis (PCA) and principal component regression (PCR) were used to analyze the data [39,40]. PCR was used to construct calibration models to predict Ang II dose from spectra of the aortas. A cross-validation routine was used with NIR spectra to assess the statistical significance of the prediction of Ang II dose and collagen/elastin in mice aortas. The accuracy of the PCR method in predicting Ang II dose from NIR spectra was determined by the F test and the standard error of performance (SEP) calculated from the validation samples. 

The Standard Error of Prediction (SEP) is supposed to refer uniquely to those situations when a calibration is generated with one data set and evaluated for its predictive performance with an independent data set. Unfortunately, there are times when the term SEP is wrongly applied to the errors in predicting y variables of the same data set which was used to generate the calibration. Thus, when we encounter the term SEP, it is important to examine the context in order to verify that the term is being used correctly. SEP is simply the square root of the Variance of Prediction, s2. The RMSEP (see below) is sometimes wrongly called the SEP. Fortunately, the difference between the two is usually negligible. 

Figure 4.10 Effect of reduced glutathione (GSH) (0-1.0 mM) on Na/K ATPase inhibition associated with the addition of oxidized glutathione (GSSG) (1 me). Experiments were performed using an isolated bovine ventricular Na/K ATPase preparation. Na/K ATPase activity was quantified by the ouabain-sensitive hydrolysis of ATP to yield inorganic phosphate. The data are presented as means standard errors of the means (n = 6).

Once the standard error of estimate of the mean forecasted response has been estimated, i.e., the uncertainty in the total production rate, one can compute the probability level, a, for which the minimum total production rate is below some pre-determined value based on a previously conducted economic analysis. Such calculations can be performed as part of the post-processing calculations. 

Table 33-1 Summary of results obtained from synthetic linearity data using one PCA or PLS factor. We present only those performance results listed by the data analyst as Correlation Coefficient and Standard Error of Estimate...

Statistical analysis Statistical analysis consists of determination of Standard error of means (SEM) or the Student- t-testing. The measurement error was about 1-2% (10 spectra per one variant, n=10). Counting was performed in four or five replicates (the number of Petri dishes per a treatment). SEM for the fluorescence spectra was 2 %. 

FIGURE 4.6 Double CV with three segments (tout) in the outer CV and four segments (%) in the inner CV. In the outer CV, test sets are defined and the prediction performance for new cases is estimated (for instance the standard error of prediction, SEPtest). In the inner CV, the optimum complexity of the model is estimated from a calibration set as shown in Figure 4.5. 

Biological assays were performed with 6 mM compound in the diet. The reproductive index of aphids fed with 12 mM of glycine-betaine was 5.1 after 72 h of feeding. Values shown are the average ( standard error) of three samples of ten aphids each. Reproduction studies were performed with five samples. 

The optimization of a freq, Ot time and y is performed using the subjective audio quality database that resulted from the ISO/MPEG 1990 audio codec test [ISO90, 1990]. The optimization used the standard error of the estimated MOS from a third order regression line fitted through the PAQM, MOS datapoints. The optimization was carried out by minimization of the standard error of the estimated MOS as a function of O.freq, (X time, Y... 

The statistical uncertainty arising from the analytical measurement is derived from the automatic data collection procedure noted before. The AGAS computer performs a standard error analysis and produces both a mean and the standard error of the mean associated with that value. A computer program is used to combine the uncertainties from the primary gravimetric process with the uncertainties produced from the standard deviation of the instrument s response for each of the gas mixtures. 

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