Statistical results

Subroutine OUTDAT. OUTDAT prints the estimated parameters and other statistical results obtained during the regression. 

This section describes a minimal theoretical background so you can understand the process of creating a classical molecular dynamics trajectory and use it to obtain a visual or statistical result. 

Figure 4 illustrates the trend in adiabatic flame temperatures with heat of combustion as described. Also indicated is the consequence of another statistical result, ie, flames extinguish at a roughly common low limit (1200°C). This corresponds to heat-release density of ca 1.9 MJ/m (50 Btu/ft ) of fuel—air mixtures, or half that for the stoichiometric ratio. It also corresponds to flame temperature, as indicated, of ca 1220°C. Because these are statistical quantities, the same numerical values of flame temperature, low limit excess air, and so forth, can be expected to apply to coal—air mixtures and to fuels derived from coal (see Fuels, synthetic). 

An appreciation of statistical results can be gained from a study conducted to support the first application of computer control for an ethylene oxide production unit at Union Carbide Corporation in 1958. For the above purpose, twenty years of production experience with many units was correlated by excellent statisticians who had no regard for kinetics or chemistry. In spite of this, they did excellent, although entirely empirical work. One statement they made was ... [ethane has a significant effect on ethylene oxide production.] This was rejected by most technical people because it did not appear to make any sense ethane did not react, did not chemisorb, and went through the reactor unchanged. 

The validity of the risk of nuclear that was estimated by the Reactor Safety Study was questioned when the TMI-2 accident occurred. This showed a misunderstanding of the probabilistic nature of risk, A single event neither proves nor disproves a statistical result it may, however, question the usefulness of risk as a safety measure. 

One attraction of MD simulation is the possibility of computer animation. The mobility of ions inside a charged cylindrical pore can be visualized. Some movie clips of EMD and NEMD are downloadable at http //chem.hku.hk/ kyc/movies/. mpg. Some features that escape statistical averages can be learned in watching the animation. While the coions are present mainly in the center of the pore, occasional collisions with the wall do occur, as observed in the movie. The time scale of a coion staying near the wall is of the order of 1 ps, compared to 10 ps for the counterion. While the averaged equilibrium distributions indicate an infinitesimal concentration of coion at the wall, reaction of coion with the wall can occur within a time scale of 1 ps. From the video, it can also be observed that the radial mobility of the counterion is more significant compared to the coion s and compared to the axial mobility. It is consistent with the statistical results. 

Thus, the two bosons have an inereased probability density of being at the same point in spaee, while the two fermions have a vanishing probability density of being at the same point. This eonelusion also applies to systems with N identieal partieles. Identical bosons (fermions) behave as though they are under the influence of mutually attractive (repulsive) forces. These apparent forces are called exchange forces, although they are not forces in the mechanical sense, but rather statistical results. 

Using Eqs. (5-42)-(5-46) in Section 5.3.2.2 with iterative calculations, the predicted CHF were compared with Columbia University data (Fighetti and Reddy, 1983). The comparison was made by examining the statistical results of critical power ratios (DNBRs), where... 

Table 5.15 Statistical results of DNBR for six simple bundles...

Table 5.16 Statistical results of DNBR for test sections 38, 58, and 60...

Statistics available in the system include a large set of commonly used analysis techniques, as well as advanced nonlinear curve fitting techniques. Statistical results can be displayed numerically or graphically. 

Further analysis yielded new models for each of the chemical classes with improved statistical significance. The final model for nonaromatics contained six descriptors and had an Rs of 0.932 (leave-one-out 0.878), the final model for the aromatics contained 21 descriptors and had an Rs of 0.942 (leave-one-out 0.823), and the final model for the heteroaromatics contained 13 descriptors and had an Rs value of 0.863 (leave-one-out 0.758). These statistical results were considered reliable enough for the models to be regarded as predictive. The analysis did yield some interesting insights into the impact of various structural fragments on human oral bioavailability. However, these observations were based on the sign of the coefficient and so must be treated with some caution. 

The experimental results obtained by Chinese scientists obviously show that the areas suffering from acid rain in China have extended northwards from the south of the Yangtze River in 1986 to the whole East China at present. The statistical results from the Acid Rain Survey in 82 cities from 1991 to 1995 indicate that the annual average pH value of the precipitation was lower than pH 5.6 in nearly half of these cities or in 87% of the southern cities, which are located in the south to the Qingling... 

Peter Filzmoser was bom in 1968 in Weis, Austria. He studied applied mathematics at the Vienna University of Technology, Austria, where he wrote his doctoral thesis and habilitation, devoted to the field of multivariate statistics. His research led him to the area of robust statistics, resulting in many international collaborations and various scientific papers in this area. His interest in applications of robust methods resulted in the development of R software packages. J ( He was and is involved in the organization of several y scientific events devoted to robust statistics. Since... 

The data were modeled by a principal components model with three components. The statistical results method (25. 31) are presented in Table IV and V. In addition, the measured total PCB concentration is included in Table IV. One of the three sets of two-dimension plots (Theta 1 vs Theta 2) is presented in Figure 10. Individual samples of a given Aroclor were distributed regularly in these plots and samples were ordered according to concentration. The sums of squares decreased from 4,360 to 52.4 (Table V.) and approximately 88 percent of the standard deviation was explained by the three term component model. 

The normal distribution has some properties that are very important in understanding statistical results. The curve is symmetrical about the central value p. 68,27% of the values he widiin p + la, 95,45% within p + 2a and 99,73% within p + 3a. 

We should look for strange data, which e g. make no sense from a scientific point of view. Maybe we can see that there is no need at all for a significance test. We can crosscheck the statistical result with our common sense visual appraisal. And the most essential point we possibly can see, that there is statistical significance but the difference is not important in magnitude compared with our quality needs. 

Compare the statistical result with a commonsense visual appraisal... 

In its order of magnitude, this value of b0 coincides with the statistical result. (The difference between the two derivations is that in the second one a translatory degree of freedom is replaced by a vibrational degree of freedom for the adsorbed state.)... 

Molecular structure data bases are particularly useful in the analysis and engineering of zinc coordination polyhedra, and statistical results from the Brookhaven Protein Data Bank (Bernstein et al., 1977) and the Cambridge Structural Database (Allen et al., 1983) are presented... 

These limitations on the statistical inference of species contributions to the particle light extinction coefficient raise several questions (i) Is the statistical analysis of filter data a valid method for determining species contributions to the extinction coefficient of atmospheric aerosols (ii) Can we place confidence limits on the quality of the statistical results and (iii) Can the quality of the statistical results be enhanced through improved sampling techniques ... 

In summary, the variance in the measured fine particle scattering coefficient, bgp was dominated by sulfate concentrations. Organics and crustal species were much less important statistically. The inferred mass scattering effeciency for sulfates was intermediate between other desert values and Los Angeles. The statistical results for China Lake are quite similar to those by other investigators at other locations, even though only the fine aerosol was sampled at China Lake. 

Human perception of flavor occurs from the combined sensory responses elicited by the proteins, lipids, carbohydrates, and Maillard reaction products in the food. Proteins Chapters 6, 10, 11, 12) and their constituents and sugars Chapter 12) are the primary effects of taste, whereas the lipids Chapters 5, 9) and Maillard products Chapter 4) effect primarily the sense of smell (olfaction). Therefore, when studying a particular food or when designing a new food, it is important to understand the structure-activity relationship of all the variables in the food. To this end, several powerful multivariate statistical techniques have been developed such as factor analysis Chapter 6) and partial least squares regression analysis Chapter 7), to relate a set of independent or "causative" variables to a set of dependent or "effect" variables. Statistical results obtained via these methods are valuable, since they will permit the food... 

Bias an effect which systematically distorts a statistical result. 

Comparative Molecular Field Analyses of Artemisinin Databases — Statistical Results of Partial Least Squares (PLS) Analyses... 

Many questions can arise when considering the validity of a statistical result. 

Statistical Results from the Analysis Methods. Continuous time vs. relative intensity curves were made spectrometrically for each of 11 elements in seven different coal ash samples. The results showed that peak intensities for all the elements in each sample were generally reached between 50 and 60 sec after initiation of the arc. This behavior helps to explain why using iron as the variable internal standard was successful for the normally wide range of volatilities represented. The large dilution factor involved or a possible carrier distillation effect of barium nitrate might explain the almost complete absence of fractional volatilization. 

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