Root mean square deviation error

The Tb abundance in meteorites is assumed to be 0.5 ppm. Errors for the Danish Cretaceous (3 samples) and Tertiary (3 samples) HNO,-insoluble residues are root-mean-square deviations. Errors for the HNO,-insoluble residues from the Gubbio and Danish boundary layers are 1 a values of the counting errors. Key , Gubbio boundary layer residue O, Danish Cretaceous residues < >, Danish Tertiary residues and , Danish... 

RMS root mean square deviation error V frequency... 

The quantity [Xed/ (2J + 1)] ed is sometimes denoted as and can be compared directly with the experimental dipole strength of transition i. The root mean square deviation error RMS is a measure for the goodness of the fit ... 

The analytical results for each sample can again be pooled into a table of precision and accuracy estimates for all values reported for any individual sample. The pooled results for Tables 34-7 and 34-8 are calculated using equations 34-1 and 34-2 where precision is the root mean square deviation of all replicate analyses for any particular sample, and where accuracy is determined as the root mean square deviation between individual results and the Grand Mean of all the individual sample results (Table 34-7) or as the root mean square deviation between individual results and the True (Spiked) value for all the individual sample results (Table 34-8). The use of spiked samples allows a better comparison of precision to accuracy, as the spiked samples include the effects of systematic errors, whereas use of the Grand Mean averages the systematic errors across methods and shifts the apparent true value to include the systematic error. Table 34-8 yields a better estimate of the true precision and accuracy for the methods tested. 

Each abundance was divided by the abundance of that element (except for Rh) in Type / carbonaceous chondrites. Rh abundances were divided by Rh abundances in other types of chondrites as Cl values were not available. Errors in the LBL measurements reflect 1 a values of the counting errors, except for the Au error. The latter is the root-mean-square deviation of six measurements, because the six values were not consistent within counting errors. The Os measurement was on a HNO,-insoluble residue that had been fired to 800°C. Key , this work and O, previous work of Ganapathy. 

It is a straightforward matter to fit various model profiles to realistic, exact computed profiles, selecting a greater or lesser portion near the line center of the exact profile for a least mean squares fit. In this way, the parameters and the root mean square errors of the fit may be obtained as functions of the peak-to-wing intensity ratio, x = G(0)/G(comax)- As an example, Fig. 5.8 presents the root mean square deviations thus obtained, in units of relative difference in percent, for two standard models, the desymmetrized Lorentzian and the BC shape, Eqs. 3.15 and 5.105, respectively. 

The number m of these parameters must be smaller than the number of known levels n, i.e. m < n, otherwise the problem is unsolvable. If a set of parameters Rk exactly describes levels Si, and levels E, are measured accurately and identified correctly, then for finding the true values of these parameters, it would be enough to solve a system of m equations with m unknowns. In practice, due to non-observance of the above-mentioned conditions, the obtained roots of the system of m equations will not satisfy the remaining n — m equations. However, our purpose is to find values of parameters Rk, for which all equations are satisfied with the smallest error. Then the root-mean-square deviation of energy levels S, found from those Ei measured, would be minimal. 

The root mean square deviation for measured versus estimated pKa values for 214 azo dyes and related aromatic amines was 0.62 pKa units. In comparison to experimental errors... 

With a small number of measurements, calculating valid error bars requires a more complex analysis than the one given in Section 4.3. The mean is calculated the same way, but instead of calculating the root-mean-squared deviation a, we calculate the variance s ... 

Table 4-2 reports the electrostatic and non-electrostatic components of AGsoi in water for the series of compounds included in the study computed from MST calculations. The deviation between experimental and calculated free energies of hydration is in general small, as noted in a mean signed errors (mse) close to zero and a root-mean square deviation around 0.9 kcal/mol, which compares with the statistical parameters obtained in the parametrization of the MST model [15]. 

Determine the 20 predicted responses by y = D.b, and so die overall sum of square residual error, and the root mean square residual error (divide by die residual degrees of freedom). Express the latter error as a percentage of the standard deviation of the measurements. Why is it more appropriate to use a standard deviation radier than a mean in diis case ... 

Calculate the percentage root mean square prediction errors for each of the six variables as follows, (i) Calculate residuals between predicted and observed, (ii) Calculate the root mean square of these residuals, taking care to divide by 5 rather than 8 to account for the loss of three degrees of freedom due to the PLS components and the centring, (iii) Divide by the sample standard deviation for each parameter and multiply by 100 (note that it is probably more relevant to use the standard deviation than the average in this case). 

Average of three measurements. Error quoted for this value is the root mean square deviation of the three measurements. Other errors are based on the results of the least-squares fits. 

The SE(y) parameter, the standard error of the y estimate, is sometimes referred to as the RMSD (root-mean-square deviation). 

Minimization of the residual 91 in Eqn (11.40) cannot lead to the minimum of the root-mean-square deviation and the regularization function simultaneously. The regularization parameter a allows us to choose an appropriate compromise between smoothness of the PSD function and acceptable error norm. Of course, this choice is quite subjective and there are no universal recommendations. In most cases it is necessary to rely on experience and intuition. 

Root mean square error (RMSE) (or root mean square deviation, RMSD). Also known as standard error in calculation (SEC) or standard deviation error in calculation (SDEQ, it is a function of the residual sum of squares ... 

Normalized root mean square error, denoted as NRMSE (or normalized root mean square deviation, NRMSD), is defined dividing RMSE (or RMSD) by the range of the response variable ... 

Note. The terms mean square error, root mean square error, mean square deviation, root mean square deviation, and expected square error are also often defined using the word squared instead of the word square . 

When the square variable is a difference between values predicted by a model or an estimator and the values actually observed, this quantity take the name of root mean square deviation RMSD or root mean square error, RMSE) and is among the regression parameters. 

The first step in validation is simply to verify that the remaining errors in the reproduction of the reference data are acceptably small. If the weight factors have been set, as suggested earlier, to the inverse of the acceptable error for each data type, the test is particularly simple. If the final penalty function is lower than the number of data points, the root mean square (rms) error will automatically fall within the acceptable range. The data should also be divided by type and retested, to make sure that the proper balance has been obtained. As before, outliers should be carefully scmtinized. Any errors in the reference data or deficiencies in the functional form are most easily detected at this stage. Plots of calculated vs. reference data can also give valuable information on trends in remaining deviations and possible systematic errors (20). 

We compare in Table 1 our results with the experimental B2 bands and assignments [12,13], in increasing energy order. Above 10000 cm l, the errors of the calculated nonadiabatic levels are similar to the root mean square deviation (RMSD) of... 

By definition, the standard deviatirai is the root-mean-square deviation about the mean value. It does not provide an indicator of the statistical error about the mean of multiple measurements. If the distribution is unimodal and not too skewed, then the standard deviation will give a reasonable indication of dispersity.. 

In addition to defining the correlation between predicted and experimental values, we need a means of measuring the magnitude of the error in the prediction. The most commonly used error measure in the cheminformatics literature is the root-mean-square deviation (RMSD), which is also known as the RMS error [33]. If we consider paired values X and F, RMSD can be calculated using the following equation... 

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