Treatment of Data

Treatment of Data.—Typical osmotic data are shown in Figs. 38 and 39. Here the ratio ( n/c) of the osmotic pressure to the concentration is plotted against the concentration. If the solutions behaved ideally, van t Hoff s law Eq. (11) would apply and m/c should be independent of c. Owing to the large effective size of the polymer molecules in solution (Fig. 34) and the interactions between them which consequently set in at low concentrations, /c increases with c with a 

According to the theory of dilute polymer solutions, to be discussed in Chapter XII, the osmotic pressure may be expressed as a function of the concentration by an equation of the form  

If the value of g may be satisfactorily approximated by 0.25, and this usually is legitimate, then Eq. (13) may be written 

It will be observed in Fig. 38 that the slope of the x/c plot for polyisobutylene in benzene at 30°C is small and that there is no evidence of curvature. This is in accord with Eq. (13), which requires the magnitude of the curvature to vary as the square of the slope. Of more immediate importance is the fact that the same limiting values, ( /c)o, are obtained in different solvents, despite widely differing behavior at higher concentrations. Hence the observed molecular weights are independent of the solvent employed within experimental error. In 

DETERMINATION OF MOLECULAR WEIGHTS AND POLYMER DIMENSIONS BY LIGHT SCATTERING 

Treatment of Data.—Various applications of the Stern-Volmer equation 658 and the kinetic analysis of bimolecular reactions which can occur from both singlet and triplet states,666 corrections for inner filter effects on rate expressions for 

Nagase and T. Fueno, Theor. Chim. Acta, 1974, 35, 217 P. Kollman, J. McKelvey, A. 

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The LIMS software is essentially a database for tracking, reporting, and archiving lab data as well as scheduling and guiding lab activities. Graphical and statistical treatment of data for improved process control (qv) as well as preparation of certificates of analysis (COA) for the customer are some of the other features of a comprehensive LIMS package (30). 

The nuclear equipment failure rate database has not changed markedly since the RSS and chemical process data contains information for non-chemical process equipment in a more benign environment. Uncertainty in the database results from the statistical sample, heterogeneity, incompleteness, and unrepresentative environment, operation, and maintenance. Some PSA.s use extensive studies of plant-specific data to augment the generic database by Bayesian methods and others do not. No standard guidance is available for when to use which and the improvement in accuracy that is achieved thereby. Improvements in the database and in the treatment of data requires, uhstaiui.il indu.sinal support but it is expensive. 

One other attempt at a similar treatment of data merits mention. Taylor et have measured the piC values of a series of 4-substituted... 

A. Experimental Method and Treatment of Data 1. Apparatus and Procedure... 

Ludwig KR (2003) Mathematical-statistical treatment of data and errors for °Th/U geochronology. Rev Mineral Geochem 52 631-636... 

Lovley D, Philhps EJP, Gorby YA, Landa ER (1991) Microbial reduction of itraniitm. Nature 350 413-416 Lowson RT, Short SA, Davey BG, Gray DJ (1986) " U/ U and °Th/ " U activity ratios in mineral phases of a lateritic weathered zone. Geochim Cosmochim Acta 50 1697-1702 Ludwig KR (2003) Mathematical-statistical treatment of data and errors for h/U geochronology. Rev Mineral Geochem 52 631-636... 

Mathematical-Statistical Treatment of Data and Errors for Th/U Geochronology... 

Signals from detectors were monitored on-line by Virtual Bench-Lab View computation programs or labVIEW 7 programs. Treatments of data were done using Origin 6.1. 

Helsel DR (1990) Less than obvious statistical treatment of data below the detection limit. Environm Sci Technol 24 1756... 

Figure 3. Arrhenius treatment of data for experimental crosslinkers.

Firstly, a single value shall exert merely a small effect upon the mean value (x) and secondly, the treatment of data with the real statistical analysis would certainly reveal vividly the probability that the suspected out of place result is a bonafide member of the same population as the others. 

The mathematical treatment of data will produce only slight differences in the threshold values. 

Table XV. Regression Accuracy with Various Transformation Treatments of Data. Chlorothalonil Data Set.

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