Weights methods, statistical

Table I indicates good agreement between the molecular weight distribution statistics obtained by coupled GPC/Viscometer method and the nominal values for t BS 706. The discrepancy between the Mark-Houwink parameters obtained here and the reported values for polystyrene standard ( ) in THF at 25°C (i.e., a = 0,706 and k = 1.60 x 10 ) may in part be due to the uncertainty involved in the determination of the dead volume between DRI and viscometer detectors. Our simulation studies over a range of dead volume values (0 to 120u)l) showed that a and k are quite sensitive to the dead volume between the detectors. Larger dead volume results in smaller o and larger k values. This is a direct result of a clockwise rotation of log [q] vs. log M(v) curve (Figure 12) which occurs when the dead volume correction is applied in quantitative analysis. The effect on the molecular weight statistics, however, appeared to...

The energy levels in the semi-empirical conformational energy calculations may be used to derive conditional probabilities using the statistical weights method described by Flory (13). 

A number of methods are available for preselection. These include ranking and weighting, benchmarking, statistical analysis, data envelopment analysis, analytical hierarchy process, and several artificial intelligence-based methods. 

The bias-free method of performing the statistical averages on individual realizations uses the transit time, t weighting (see George, 1976). Additional information on the transit time weighting method can be found in George (1978), Buchhave et al. (1979), Buchhave (1979), and Benedict and Gould (1999). In the literature, transit time is sometimes referred to as residence time. 

It is preferable to evaluate the external event hazard on a probabilistic basis. The frequency of occurrence of the parameters describing the severity of the external hazard (such as earthquake ground acceleration, wind speed, water elevation) is estimated by probabilistic methods. Statistical parameters used for extreme events include return period and annual probability of exceedance. The hazard from other rare external events such as accidental aircraft crashes or explosions reflects the frequency of occurrence of an event with postulated characteristics (quantity of explosive material, weight and velocity of the missile, etc.), as proper statistics may not be available for the area of interest. Performance goals depend on the external event categorization as defined in Section 2. For practical use they can be approximated by deriving the product (for continuous hazard levels it can be the convolution) between the annual probability of exceedance of an external event and the Pp induced by that specific external event. Probability values for performance... 

Using this concept, Burdett developed a method in 1955 to obtain the concentrations in mono-, di- and polynuclear aromatics in gas oils from the absorbances measured at 197, 220 and 260 nm, with the condition that sulfur content be less than 1%. Knowledge of the average molecular weight enables the calculation of weight per cent from mole per cent. As with all methods based on statistical sampling from a population, this method is applicable only in the region used in the study extrapolation is not advised and usually leads to erroneous results. 

US model can be combined with the Monte Carlo simulation approach to calculate a r range of properties them is available from the simple matrix multiplication method. 2 RIS Monte Carlo method the statistical weight matrices are used to generate chain irmadons with a probability distribution that is implied in their statistical weights. 

Vitha, M. F. Carr, P. W. A Laboratory Exercise in Statistical Analysis of Data, /. Chem. Educ. 1997, 74, 998-1000. Students determine the average weight of vitamin E pills using several different methods (one at a time, in sets of ten pills, and in sets of 100 pills). The data collected by the class are pooled together, plotted as histograms, and compared with results predicted by a normal distribution. The histograms and standard deviations for the pooled data also show the effect of sample size on the standard error of the mean. 

Another important aspect of the fatigue of all materials is the statistical nature of the failure process and the scatter which this can cause in the results. In a particular sample of plastic there is a random distribution of microcracks, internal flaws and localised residual stresses. These defects may arise due to structural imperfections (for example, molecular weight variations) or as a result of the fabrication method used for the material. There is no doubt that failure... 

While all methods of single and double point are used to characterize a polymer solution is always advisable to increase the statistical weight (to reduce errors) with at least four different concentrations of polymer in a given solvent. 

Rodbard, D, Estimation of Molecular Weight by Gel Filtration and Gel Electrophoresis II. Statistical and Computational Considerations. In Methods of Protein Separation Catsimpoolas, ed. Plenum Press New York, 1976 Vol. 2, p 181. 

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