Statistical graphical methods

The methods discussed have been called Graphical Statistical Methods since ... 

A few other methods of determining the ring content of saturated mineral oil fractions will be discussed further on in connection with the application of the viscosity in the field of graphical statistical methods. 

III. APPLICATION OF GRAPHICAL STATISTICAL METHODS IN THE DETERMINATION OF THE COMPOSITION OF GLASSES AND SILICONES... 

In the last few years the graphical statistical methods have been successfully applied not only to petroleum, fatty oils and coal, but also to glass and silicones. Though the recently developed methods for glass and silicones are still in their initial stages, some remarkable results have already been obtained. 

VI. GRAPHICAL STATISTICAL METHODS FOR STUDYING CATALYTIC PROCESSES. CHARACTERIZATION OF CATALYSTS BY PARAMETERS... 

GRAPHICAL STATISTICAL METHODS OF IDENTIFICATION OF MINERAL AND FATTY OILS, GLASS, SILICONES, AND CATALYSTS... 

Visser, S. A. (1983a). Application of Von Krevelen s graphical-statistical method for the study of aquatic humic material. Environ. Sci. Technol. 17, 412-417. 

Van Krevelen, DW. (1950). Graphical-statistical method for the study of structure and reaction processes of coal. Fuel, Vol.29, pp. 269-284. 

The goal of EDA is to reveal structures, peculiarities and relationships in data. So, EDA can be seen as a kind of detective work of the data analyst. As a result, methods of data preprocessing, outlier selection and statistical data analysis can be chosen. EDA is especially suitable for interactive proceeding with computers (Buja et al. [1996]). Although graphical methods cannot substitute statistical methods, they can play an essential role in the recognition of relationships. An informative example has been shown by Anscombe [1973] (see also Danzer et al. [2001], p 99) regarding bivariate relationships. 

Brooks, S. P.,. Gelman, A. (1998). Alternative methods for monitoring convergence of iterative simulations. Journal of Computational and Graphical Statistics, 7, 434-455. 

The Kaplan-Meier estimates produce a step function for each group and are plotted over the lifetime of the animals. Planned, accidentally killed, and lost animals are censored. Moribund deaths are considered to be treatment related. A graphical representation of Kaplan-Meier estimates provide excellent interpretation of survival adjusted data except in the cases where the curves cross between two or more groups. When the curves cross and change direction, no meaningful interpretation of the data can be made by any statistical method because proportional odds characteristic is totally lost over time. This would be a rare case where treatment initially produces more tumor or death and then, due to repair or other mechanisms, becomes beneficial. 

Graphical methods in connection with pattern recognition algorithms, i.e. geometrical or statistical methods, e.g. minimum spanning tree or cluster analysis, are more powerful methods for explorative data analysis than graphical methods alone. 

To compare and evaluate different kinds of models created during the model development process graphical and statistical methods should be applied. A good description of the model building process can be found elsewhere [14]. 

Now we wish to pursue the pictorial presentation of Fig. 2.3 in a mathematical manner that permits us to retain explicitly the quantum features that tend to be obscured in the graphical presentation. In more explicit terms, this corresponds to an incoherent superposition of the magnetizations of individual spins or of individual sets of N interacting spins (spin systems). Incoherent or random motions are commonly treated by statistical methods that deal with an ensemble of molecules, each containing N interacting spins. 

Significant effects, i.e. effects that are significantly larger than could be due to experimental variability, can be identified by means of both graphical and statistical methods. The graphical method that is used most often is the normal probability plot explained in the preceding section (Fig. 6.9). The statistical tests are often based on a /-test, where the test statistic can be written as... 

The results of acute toxicity tests are reported as the LC50 and EC50 (concentration that reduces growth 50%) values and their 95% confidence intervals. Probit analysis is the most commonly used statistical method to determine LC50 values. Graphical interpolation can be used to estimate the LC50 value where the proportion of deaths versus the test concentration is plotted for each observation time. 

MATC — Maximum allowable toxicant concentration determined by graphical or statistical methods. 

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