Consistency testing standard deviation calculation

Breindl et. al. published a model based on semi-empirical quantum mechanical descriptors and back-propagation neural networks [14]. The training data set consisted of 1085 compounds, and 36 descriptors were derived from AMI and PM3 calculations describing electronic and spatial effects. The best results with a standard deviation of 0.41 were obtained with the AMl-based descriptors and a net architecture 16-25-1, corresponding to 451 adjustable parameters and a ratio of 2.17 to the number of input data. For a test data set a standard deviation of 0.53 was reported, which is quite close to the training model. 

There are several mathematically different ways to condnct the minimization of S [see Refs. 70-75]. Many programs yield errors of internal consistency (i.e., the standard deviations in the calculated parameters are due to the deviations of the measured points from the calculated function), and do not consider external errors (i.e., the uncertainty of the measured points). The latter can be accommodated by weighting the points by this uncertainty. The overall rehabU-ity of the operation can be checked by the (chi square) test [71], i.e., S (L + N - ) should be in the range 0.5-1.5 for a reasonable consistency between the measured points and the calculated parameters. 

Figure 12.1 shows how well the predicted results agree with the experimental values listed in Table 12.2. The predictions consistently overestimate experimental dielectric constant values for this series of samples. The difference varies from 12 to 27% of the experimental values. Qualitatively, predictions follow the same trend as experiment. The calculated slope for the best straight-line fit through the data points is equal to 0.822 with a standard deviation of 0.088. The correlation coefficient is equal to 0.881. For several of the polyimides tested here the method... 

The variation of sensitivity between different sensors was also checked. Calibration curves with five different sensors were performed. A Relative Standard Deviation of 13, 13 and 42% of calibration slopes (sensitivity) were obtained for Cu, Pb and Cd respectively. These variations should have limited consequence on bias and precision when the standard addition method is used. However, for Cd, variations in the limit of quantification between two electrodes could be expected. Finally, the accuracy of the method was evaluated by the measurement of a SWIFT reference material used during the 2nd SWIFT-WFD Proficiency Testing exercise (Table 4.2.2). The reference value was chosen as the consensus value of the selected data population obtained after excluding the outliers. The performances of the device were estimated according to the Z-score (Z) calculation. Based on this score, results obtained with the SPEs/PalmSens method were consistent with those obtained by all methods for Pb and Cu ( Z < 2) while the result was less satisfactory for Cd (2 < Z < 3). 

Further discussion on the numerical criteria to be used for evaluating TPIs can be found in ASTM standard D 6792. Some laboratories prefer to compare their standard deviation against the test method reproducibility or to use an inverse calculation from that given above. In either case an individual best laboratory will consistently produce a superior precision compared to the industry average precision. Such periodic performance feedback should be a key feature of any continuous improvement program. 

Let s look again at Table 4-2 and ask whether the two mean values of 36.14 and 36.20 mM are significantly different from each other. We answer this question with the t test. If the F test tells us that the two standard deviations are not significantly different, then for data sets consisting of n and 2 measurements (with averages jci and JC2), calculate t from the formula... 

Each of the required three individual values for each nuclide was corrected with the factor that resulted from the weights of labelled and imlabelled spinach powder. The arithmetic mean and standard deviation for each laboratory was calculated. The data were visually inspected for outlier elimination. In addition, outliers were identified using Mandel s wilhin- and between-laboratory consistency test statistic k and A-values, respectively) and Grubbs I and II tests according to DIN ISO 5125-2 The outher-free data sets were used to calculate repeatability and reproducibility. Individual z-scores were used as a measure of performance characteristic of the participating laboratories. ... 

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