Standardized mean absolute

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... 

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. 

To examine the fitness of the kinetic model CAER used for study of the water effect, we conducted model discrimination using the kinetic data of 15% Co/Si02 by comparing values of the standard function of mean absolute relative residual (MARR), which is simply defined as... 

Table 1.12 Statistical measures of errors for extrapolated CCSD(T) AEs relative to experiment (kJ/mol). A is the mean error, Astd is the standard deviation around the mean error, Aabs is the mean absolute error, and Amax is the maximum absolute error.

Baertschi P (1976) Absolute content of standard mean ocean water. Earth Planet Sci Lett 31 341-344... 

Konno and Yamazaki (1991) proposed a large-scale portfolio optimization model based on mean-absolute deviation (MAD). This serves as an alternative measure of risk to the standard Markowitz s MV approach, which models risk by the variance of the rate of return of a portfolio, leading to a nonlinear convex quadratic programming (QP) problem. Although both measures are almost equivalent from a mathematical point-of-view, they are substantially different computationally in a few perspectives, as highlighted by Konno and Wijayanayake (2002) and Konno and Koshizuka (2005). In practice, MAD is used due to its computationally-attractive linear property. 

Ptofil Risk (Measured by Standard Deviation and Recourse Penally Costs Risk (Measured by Mean-Absolute Deviation... 

Calibration methods I modified luminol standard II absolute calibration HI Hastings-Weber light standard IV luminol standard V mean value obtained by different determination methods, including chemical titrations VI triplet yield of 0.3 E mol for TMD, obtained with DBA. 

None of the semi-empirical models perform as well as Hartree-Fock models (except STO-3G), local density models, density functional models or MP2 models. PM3 provides the best overall description, although on the basis of mean absolute errors alone, all three models perform to an acceptable standard. Given the large difference in cost of application, semi-empirical models clearly have a role to play in structure determination. 

In terms of mean absolute deviation from the standard , two of the three semi-empirical models are as successful as any of the Hartree-... 

Overall, the performance of Hartree-Fock models is very poor. In most cases, activation energies are overestimated by large amounts. This is not surprising in view of previous comparisons involving homolytic bond dissociation energies (see Table 6-2), which were too small. In terms of mean absolute deviation from the standard (MP2/6-311+G ) calculations, STO-3G yields the poorest results and 3-2IG the best results. 6-3IG and 6-311+G models provide nearly identical activation energies (just as they did for transition-... 

The mass number gives the total number of protons and neutrons in an atom of an element, but it does not convey the absolute mass of the atom. To work with the masses of elements, we use comparative masses. Initially, Dalton and the other pioneers of the atomic theory used the lightest element hydrogen and compared masses of other elements to hydrogen. The modern system uses C-12 as the standard and defines one atomic mass unit (amu) as 1/12 the mass of one C-12 atom. One amu is approximately 1.66 X 10 g. This standard means the masses of individual protons and neutrons are slightly more than 1 amu as shown in Table 4.6. 

Spreadsheet 2.1. Calculation of mean, standard deviation, median, and mean absolute deviation of titration data with outlier, and after correction (shaded cells show the change from 11.02 to 10.02). 

MAD, mean absolute difference MARD, mean absolute relative difference SD, standard deviation SE, standard error SRE standard relative error. 

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