Mean absolute relative difference calculation

In addition, all the paired points (n) including the concentrations measured from the glucose sensor, [glucose] sensor, and the reference glucose measurement, [gluco-se reference, in the correlation plot are used to calculate the overall mean absolute relative difference (MARD). The median MARD is the median relative difference among all the measured values. 

A comparison of calculated and experimental anion geometries are provided in Table 5-16. Included are Hartree-Fock models with STO-3G, 3-21G, 6-31G and 6-311+G basis sets, local density models, BP, BLYP, EDFl and B3LYP density functional models and MP2 models, all with 6-31G and 6-311+G basis sets, and MNDO, AMI and PM3 semi-empirical models. Experimental bond lengths are given as ranges established from examination of distances in a selection of different systems, that is, different counterions, and mean absolute errors are relative to the closest experimental distance. 

Table 4-3, with partition coefficient estimation results for 13 aroma compounds partitioned between polyethylene (PE) and ethanol, shows an example of the estimation accuracy one can expect comparing UNIFAC to experimental data and the other partition coefficient estimation methods (Baner, 1999). In order to compare the different estimation methods, average absolute ratios of calculated to experimental values were calculated partitioned substances. When the calculated values are greater than experimental values the calculated value is divided by the experimental value. For calculated values less than the experimental values the inverse ratio is taken. Calculating absolute ratios gives a multiplicative factor indicating the relative differences between values of the experimental and estimated data. A ratio of one means the experimental value is equal to the estimated value. 

Fig. 15.2 Mean observed (a) and calculated (b) concentrations for sulphates in 2000, and absolute (c) and relative (d) differences. Unit pg S...

The G4 method is an improvement on G3 and differs from G3 as follows G4 uses an extrapolation procedure [Eq. (15.23)] to estimate the Hartree-Fock energy in the complete-basis-set limit uses a larger basis set replaces the QCISD(T) calculation by a CCSD(T) calculation uses B3LYP/6-31G(2df,p) to find the equilibrium geometry and the zero-point energy and includes two additional empirical parameters in the higher-level correction [L. A. Curtiss et al., J. Chem. Phys., 126, 084108 (2007)]. For the G3/05 test set, G4 has a mean absolute error of 0.83 kcal/mol, compared with 1.13 kcal/mol for G3. Relative computation times for benzene are 2 for G2, 1 for G3, and 3 for G4. 

Plots of all available data points in relative units are shown in Figs. 9-11. Average reference profiles of the different species were obtained by means of a spline fit procedure applied to the respective data points. Table 1 contains pertinent information for every individual halocarbon on tropospheric abundances. With the help of these, absolute profiles can be calculated for any of the substances shown. 

This finite renormalization has two consequences. First, the nonuniver-sal parameters depend on both the microscopic system and the renormalized theory chosen. They thus have no direct microscopic meaning. Physical information is contained in the relative change upon changing the chemical microstructure or temperature, but not in the absolute values. Second, on a more technical level, numerical results of finite order calculations will differ for different renormalization schemes. This is a principle problem, unavoidable in low order calculations of scaling functions. Unambiguous results are foimd only for quantities not involving the nonuniversal constants, like exponents or critical ratios, or normalized scaling functions expressed in terms of RG-invariant variables. The function P pRa) (Eq. (11.52)) is an example. For such quantities the e-expansion is unique. This aspect will be discussed further in Sect. 12.4. 

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