Mean absolute deviations

The method of drying, type of samples, Mean Absolute Deviation, Mean Absolute Percentage Error, Mean Squared Deviation of these models used for moisture content change with time are presented in Table 1. 

In Figure 15.6 we have, for the eight calculated equilibrium bond angles in the test set, plotted the mean errors, standard deviations, mean absolute errors and maximum absolute errors relative... 

Standard Deviation The absolute standard deviation, s, describes the spread of individual measurements about the mean and is given as... 

The square root of the variance is the standard deviation. The mean absolute error MAE is... 

For sources having a large component of emissions from low-level sources, the simple Gifford-Hanna model given previously as Eq. (20-19), X = Cqju, works well, especially for long-term concentrations, such as annual ones. Using the derived coefficients of 225 for particulate matter and 50 for SO2, an analysis of residuals (measured minus estimated) of the dependent data sets (those used to determine the values of the coefficient C) of 29 cities for particulate matter and 20 cities for SOj and an independent data set of 15 cities for particulate matter is summarized in Table 20-1. For the dependent data sets, overestimates result. The standard deviations of the residuals and the mean absolute errors are about equal for particulates and sulfur dioxide. For the independent data set the mean residual shows... 

The mean absolute deviation from experiment (MAD) the ave difference between the computed and experimental values ignoring sign. This is a much better measure of how well a method performed ac the calculation set. 

We are now in a position to examine the relative accuracies of a variety of different model chemistries by considering their performance on the G2 molecule set. The following table lists the mean absolute deviation from experiment, the standard deviation and the largest positive and negative deviations from experiment for each model chemistry. The table is divided into two parts the first section lists results for single model chemistries, and the remaining sections present results derived from... 

This same data is plotted in the chart on the following page. The mean absolute deviation and standard deviation are plotted as points with error bars, and the shaded blocks plot the largest positive and negative-magnitude errors. 

Ihi mcdel chanisfries in this table are arranged in ascending order ef mean absolute deviation. The other columns give the standard de-riotico of the MAD and the absolute value of the maximum error with respect to experiment for each mcdel chemistry. 

The main difference between the G2 models is tlie way in which tlie electron correlation beyond MP2 is estimated. The G2 method itself performs a series of MP4 and QCISD(T) calculations, G2(MP2) only does a single QCISD(T) calculation with tlie 6-311G(d,p) basis, while G2(MP2, SVP) (SVP stands for Split Valence Polarization) reduces the basis set to only 6-31 G(d). An even more pruned version, G2(MP2,SV), uses the unpolarized 6-31 G basis for the QCISD(T) part, which increases the Mean Absolute Deviation (MAD) to 2.1 kcal/mol. That it is possible to achieve such good performance with tliis small a basis set for QCISD(T) partly reflects the importance of the large basis MP2 calculation and partly the absorption of errors in the empirical correction. 

A comparison between Gl, G2, G2(MP2) and G2(MP2,SVP) is shown in Table 5.2 for the reference G2 data set the mean absolute deviations in kcal/mol vary from 1.1 to 1.6 kcal/mol. There are other variations of tlie G2 metliods in use, for example involving DFT metliods for geometry optimization and frequency calculation or CCSD(T) instead of QCISD(T), with slightly varying performance and computational cost. The errors with the G2 method are comparable to those obtained directly from calculations at the CCSD(T)/cc-pVTZ level, at a significantly lower computational cost. ... 

Geometry level at whieh the strueture is optimized higher-order eon-elation method(s) for estimating higher-order eorrelation effeets thermo level at which the thermodynamieal eoneetions are ealeulated [vibrational seale factor] MAD Mean Absolute Deviation for reference data set in kcal/mol. 

Gradient corrected methods usually perform much better than LSDA. For the G2-1 data set (see Section 5.5), omitting electron affinities, the mean absolute deviations shown in Table 6.1 are obtained. The improvement achieved by adding gradient terms is impressive, and hybrid methods (like B3PW91) perform almost as well as the elaborate G2 model for these test cases. For a somewhat larger set of reference data, called the G2-2 set, the data shown in Table 6.2 are obtained. 

Table 6.1 Comparison of the performance of DFT methods by mean absolute deviations (kcaPmol)...

Method Mean absolute deviation Maximum absolute deviation... 

MINDO/3 methods clearly have severe problems with some of the conjugated systems. The MNDO/AM1/PM3 family perform somewhat better, although none of them can predict the correct ordering. The SAMI method is not an improvement for this case. The mean absolute deviation (MAD) for the predicted stabilities is 10kcal/mol, which is a typical accuracy for semi-empirical methods. 

Fig. 3.46 Dynamical pivfiles for graph sequences Gs (defined in section 3.3.2), representing averages over Ng sequence samples. The x-axis labels each g G Gs, dashed lines denote pure range-r topologies r with gi = range-1, 1-dira lattice and vertical bars give the mean absolute deviations of a particular rneasiire. Each system has size. N = 12, with Ng and rules TZ as follows (a) Ng = 50, K = OTIO, (b) Ng = 25, Ti= OT26, (c) Ng = 50, 7 = T16, (d) dg = 50, 7 = T4.

Deviation Variation from the a specified dimension or design requirement, usually defining the upper and lower limits. The mean deviation (MD) is the average deviation of a series of numbers from their mean. In averaging the deviations, no account is taken of signs, and all deviations whether plus or minus, are treated as positive. The MD is also called the mean absolute deviation (MAD) or average deviation (AD). 

Mean absolute deviation MAD is a statistical measure of the mean (average) difference between a product s forecast and actual usage (demand). The deviations (differences) are included without regard to whether the forecast was higher than actual or lower. 

Firstly, the krlglng estimator is optimal only for the least square criterion. Other criteria are known which yield no more complicated estimators such as the minimization of the mean absolute deviation (mAD), E P(2c)-P (3c), yielding median-type regression estimates. 

Table 8-3. Mean absolute deviations from experiment for computed bond lengths [A]. Taken from Scheiner, Baker, andAndzelm, 1997. 

Table 8-4. Compilation of mean absolute deviations for bond lengths [A] / bond angles [degrees] for small main group molecules from different sources.

Table 9-3. Mean absolute deviations (MAD) from experiment [kcal/mol] for 44 atomization energies and number of results that deviate by less than 5, between 5 and 10, and over 10 kcal/mol from experiment. Taken from Martell, Goddard, and Eriksson, 1997. 

Table 9-12. Compilation of mean absolute (maximum) deviations for ionization energies [eV] of small main...

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