Absolute average relative deviation

Functional and method Average (absolute) deviation Average relative deviation comment... 

Functional and methodf Average deviation Average absolute deviation Average relative absol. deviation comment... 

Later, they compared the performance of different density-functional schemes.38 They found that the average absolute deviation could be reduced from about 91 kcal mol-1 for a specific LDA to 7-20 kcal mol-1 for different types of GGA, and further to about 3 kcal mol 1 for the best hybrid methods. This should not be taken as a surprise since the parameters of the hybrid functionals (i.e., the relative weighting of Hartree-Fock and density-functional exchange) are often determined by optimizing this performance. Petersson et al.39 have later argued that the error for the hybrid methods in fact can be reduced even further to about 1.5 kcal mol 1. 

Ibpoi, Tawa, and Burt t 352J estimated the absolute and relative acidities Df substituted imidazoles using DFT and high-level ab initio methods with a self-consistent reaction field solvent model. They were able to determine the acidities within an average absolute deviation of 0.8 pK units. 

Table 11.11 Maximum intensities of the s- and p-PDOS values (a.u.) of the Si atoms in the VI-AI20O42 model optimized at PBE/PAW theoiy level versus the Si... Si elongation of the longest bond relative to equilibrium bulk Si-Si distance of 2.35 A (AR, A) and average absolute deviation (P, °) of the a = X-Si-X angle (X = Si or O) expressed as p = Sj=i,6 (laj -109.47°l)/6, with number of weak bonds (N) and different neighbor types of each Si atom (see Fig. 11.13)...

The best values of the parameter Cj are 1.51, 1.36, and 2.01 for no mass transfer, d and c direetion of transfer respectively. The product af is considered as the agitation variable in the equation, since the fit could not be improved if a and / were treated separately. The average absolute value of the relative deviation in the predicted values of d 2 from the experimental points is 16.3%. Even in packed columns, the separation can be substantially improved by pulsing of the continuous phase resulting from greater shear forces that reduce the drop size and increase the interfacial area [1, Chapter 8]. 

The optimized values of C are 0.63, 0.53, and 0.74 for no mass transfer, c -> <7 and c, respectively. The value of the holdup is ignored due to lack of data. Equation (9.12) predicts the drop size with an average absolute value of the relative deviation of 23%. 

The values of the constant Ci are 9.81 x 10 for no mass transfer and c d transfer, and 0.31 for d -> c transfer. The stage number which varies from 2-17 in the present set of data, shows a rather weak effect on drop size. Equation (9.13) predicts the drop diameter with an average absolute value and relative deviation of 17.6%. 

Gong and Cao described A. annua SEE of artemisinin (1) in SCCO2 determined by static method at three temperatures (313, 323 and 333 K) and pressures varying between 11 and 31 MPa. The solubility data ranged from 0.498 x 10 to 2.915 x 10 mol/mol under these conditions. Two density-based models (Chrastil s and Mendez-Sanfiago-Teja s) were selected to correlate the experimental data and the average absolute relative deviation was 8.32% and 8.33%, respectively. The correlation results were in agreement with experimental data. 

A linear solvation energy relationship (LSER) has been developed to predict the water-supercritical CO2 partition coefficients for a published collection of data. The independent variables in the model are empirically determined descriptors of the solute and solvent molecules. The LSER approach provides an average absolute relative deviation of 22% in the prediction of the water-supercritical CO2 partition coefficients for the six solutes considered. Results suggest that other types of equilibrium processes in supercritical fluids may be modeled using a LSER approach (Lagalante and Bruno, 1998). 

Other correlations have been summarized in the literature [41, 51, 58]. The proposition of Iliuta et al. [59] is, at present, far better than all the previous published correlations. The average absolute relative error is 28.1 with a standard deviation of 37%. 

In a recent overview, Iliuta et al. [59] proposed a new correlation, which estimates the liquid Sherwood number with an average absolute relative error of 22.3% and a standard deviation of 25.3%. 

The difference between the AE and the AAE is that in the average error, positive and negative errors tend to cancel each other, which makes the prediction look better than it actually may be. The average absolute error can have only a positive value, because of the absolute value function. It is a better indication of the "goodness of fit" than is the average error. A small AE and a relatively large AAE usually indicates a systematic deviation between the function (values) and the predictions (estimates). 

The data plotted in Figure 32-1 were obtained with the aid of F.quation 32-9. These curves show the deviation (.(, - p) from the true average value that would be expected if 1000 replicate observations were made on the same sample. Curve A gives the distribution for a substance for which the true average count p for a selected period is 5 curves B and C correspond to samples having true means of 15 and 35. Note that the absolute deviations become greater with increases in p, but the relative deviations become smaller. Note also the lack of. symmetry about the mean for the two smaller count numbers. 

Another quantitative measure of the ability of an equation of state to represent experimental data for a thermodynamic property is obtained from the average absolute relative deviation (AARD) that is given by ... 

To determine Ks we need to know the average mass of the cereal samples and the relative standard deviation for the %(w/w) ash. The average mass of the five cereal samples is 1.0007 g. The average %(w/w) ash and the absolute standard deviation are, respectively, 1.298% and 0.03194. The percent relative standard deviation, therefore, is... 

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