Error values

So when measuring cracks depth at the error value of less than 10%, the... 

The error, ER, would simply be the difference between the SDi and SEE equations. To be more accurate for calculating mold dimensions where the product size and shrink rate increase, this error value should be considered or Table 3-16 is be used. This table shows, as one example, which in the low shrink (0.008 mil/in. or less) materials, the products must be larger than 15 in. 

The values for K, listed here have been calculated from pK, values with more significant figures than shown so as to minimize rounding errors. Values for polyprotic acids—those capable of donating more than one proton—refer to the first deprotonation. 

The values in Table 10-6 were selected randomly, and have a mean of zero and a standard deviation of unity. When these error values are superimposed on the data, we arrive at the Table 10-7. 

Figure 43-6 Family of curves of multiplication factor as a function of Er, for different values of the parameter sigma (the noise standard deviation), for Normally distributed error. Values of sigma range from 0.1 to 1.0 for the ten curves shown, (see Color Plate 5)...

To summarize the procedure used from calculus (again, refer to either of the indicated references for the details), the errors are first calculated as the difference between the computed values (from equations 69-11) and the (unknown) true value for each individual sample these errors are then squared and summed. This is all done in terms of algebraic expressions derived from equation 69-11. The least square nature of the desired solution is then defined as the smallest sum of squares of the error values, and is then clearly seen to be the minimum possible value of this sum of squares, that could potentially be obtained from any possible set of values for the set of computed values of bt. 

The sample has been cleaned of 5 suspected binaries and of 6 stars with a 215globular cluster NGC6528 [2]. The final sample contains 217 stars. The RV distribution is shown in Figure 1. The associated errors are smaller than 0.45 km.s-1, with a mean error value of 150 m.s-1. 

The errors in the fitting parameters may be obtained from the covariance matrix of the fit if it is available, but they are more commonly estimated by varying one parameter away from its optimal value while optimizing all other parameters until a defined increase in the statistical function is obtained. However, the statistical error values obtained do not represent the true accuracies of the parameters. In fact, it is difficult to determine coordination numbers to much better than 5%, and 20% is more realistic when the data are collected at room temperature taking into account the strong coupling between the coordination number and Debye Waller terms, the error in the latter may be 30%. 

Given the matching sets of measured data, x and y, it is now possible to estimate the model regression coefficients b. Assuming that the model errors (values in f) are Gaussian-distributed, it can be proven that the value of b that minimizes the sum of squares of the model errors is determined using the least squares method ... 

Coefficient of determination for a given training set standard error / -value number of observations. 

Multiple XPS scans gave error values as 5% on atomic surface percent and + 0.2 eV on binding energy. 

Alternatively, sodium nitro prusside gives a value, close to that of dispersed silica, and, in practice, could be used to determine the total excluded volume or the kinetic dead volume without incurring serious error. Values for the kinetic dead volume measured in this way could be... 

Values are means for the number of samples indicated. All standard error values are less than 3%. Data were expressed as % of total CLA isomers. 

Predicted -j errors may be computed from Equations 4 or 5 or the graphic analysis presented below. All three methods give equivalent error values, which lends credence to the derivations. Figure 4 shows a graphic analysis of the ith property values under the constraints indicated. Curve A X, = j = -,- = 1.000... 

Relative error values for the elements ranged from zero to a high of 18% with most values being 5% or less. The 18% relative error was obtained for indium and is attributable to the low concentration of this element in the solution analyzed. Moreover, the indium values were obtained on the lower end of the working curve where the sensitivity is greatly reduced. Standard deviations and coefficients of variation for the elements of interest are at acceptable levels (less than 1% standard deviation and around 5% coefficient of variation) for this technique. Again it should be pointed out that the original purpose of the subject method was to develop a rapid routine analysis for the major and minor constituents in coal ash and related materials without the necessity of several preconcentration steps, solvent extraction techniques, or pH adjustments. 

It is of interest for variance methodology that complex values such as non dimensional Reynold s numbers and simplex were used as factors in this example. Analysis of variance has shown that all factors and interactions are important, which verifies the assumed criterion equation. The low error value of the experiment characterizes good experiment reproducibility and simultaneously indicates the fact that all essential factors have been taken into consideration. 

In the following sections, we review the application of Raman spectroscopy to glucose sensing in vitro. In vitro studies have been performed using human aqueous humor (HAH), filtered and unfiltered human blood serum, and human whole blood, with promising results. Results in measurement accuracy are reported in root mean squared error values, with RMSECV for cross-validated and RMSEP for predicted values. The reader is referred to Chapter 12 for discussion on these statistics. 

The values were determined at XenoTech (unpublished data). Constants are shown standard error (rounded to 2 significant figures, with standard error values rounded to the same degree of accuracy as the constant), and were calculated using GraFit software, which utilized rates of product formation (triplicate data) at 13 substrate concentrations. 

Here RA is the response of the analyte at unit concentration, c E is a matrix of expected, or estimated, errors and F is the Froebus norm, or root sum of the squared elements, of a matrix. It should be noted that while the NAS is a matrix quantity, selectivity (SEL), sensitivity (SEN), and signal-to-noise (S/N) are all vector quantities. The limit of detection and the limit of quantitation can also be determined via any accepted univariate definition by substituting NAS P for the analyte signal and E P for the error value. 

Table 8.19. Measured relative dipole moments of H35Cl and D35Cl. The zero error values were used as reference values for those that follow in the table...

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