Standardized mean absolute deviation

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. 

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... 

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-... 

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). 

Other parameters frequently used are the mean absolute deviation (MAD), as an estimator of the dispersion of groups of single observations, and the standard error of the mean (SEM), which is used to calculate the confidence limits of a mean value. Their formulae are presented in Eqs. 16.6 and 16.7. 

Table 24.2 Mean absolute deviations (MAD) from experiment for standard enthalpies of formation (Af/7 29g), ionization potentials (IP), electron affinities (EA), proton affinities (PA), equilibrium bond lengths irf), and harmonic vibrational frequencies (co ) computed with approximate functionals using the 6-311 ++G(3df,3pd) basis set. The fully nonempirical functionals in this table are HF, LSDA, PW91, PBE, and TPSS...

Standard key performance indicators [e.g.. Forecast accuracy, forecast quality, MAPE, Mean Absolute Deviation (MAD), Mean Squared Deviation (MSE), etc.] are used to measure forecast results, identify improvement opportunities and communicate performance to the entire organization. 

In some papers, other criteria are used. For example, sometimes standard error of prediction is used instead of (or together with) Rr. Standard error of prediction itself makes no sense until we compare it with the standard deviation for activities of the test set, which brings us back to the correlation coefficients. If used, mean absolute error (MAE) should be compared with the mean absolute deviation from the mean. Sometimes, f-ratio is calculated, which is the variance explained by the model divided by the unexplained variance. It is believed that the higher is the F-ratio, the better is the model. We suppose that when f-ratio is used, it must be always accompanied by the corresponding p-value. 

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... 

Figure 1.24. Rejection of suspected outliers. A series of normally distributed values was generated by the Monte Carlo technique the mean and the standard deviation were calculated the largest normalized absolute deviate (residual) z = xi - /.i is plotted versus n (black...

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