Statistical studies

The situation becomes more complex in the case of a three-dimensional foam. Since the septa should all be identical, again three should meet at 120° angles to form borders or lines, and four lines should meet at a point, at the tetrahedral angle of 109°28. This was observed to be the case by Matzke [179] in his extensive statistical study of the geometric features of actual foams. 

Yule G U 1944 Statistical Study of Literary Vocabulary (Cambridge Cambridge University Press)... 

At one time benzene was widely used as a solvent This use virtually disappeared when statistical studies revealed an increased incidence of leukemia among workers exposed to atmospheric levels of benzene as low as 1 ppm Toluene has replaced benzene as an inexpensive organic solvent because it has similar solvent properties but has not been determined to be carcinogenic m the cell systems and at the dose levels that benzene is... 

Note that a statistical study could be done on an electron micrograph like that shown in Fig. 1.1. The dimensions of the blobs could be converted to volumes and then to masses with a knowledge of the density of the deposited polymer. This approach could be organized into a table of classified data from which any of these averages could be calculated. 

The present statistical study has been motivated by a desire to better understand and interpret dynamic fragmentation in mechanical systems. Applications include the blasting of rock with explosives or the fragmentation caused by the impact of a high-velocity projectile. For the reasons noted earlier it is difficult to verify the present statistical theory with experiments. Recently, however, support for the theories have emerged from rather diverse sources. 

Pages 1 and 2 list all the calculation details and execute a calculation for the center point condition of the former statistical study. This is done at 70 atmospheres hydrogen, 25 atmospheres carbon monoxide, and 5 atmospheres of methanol (all partial pressures), and at 485 K temperature. This is a test case because we know that the rate is 4 mol/m s at these conditions, and this is satisfied here. 

Are statistical studies conducted to analyze the variation present in each type of measurement system and are the results used to effect a reduction in variation ... 

The inherent limitations of attribute data prevent their use for preliminary statistical studies since specification values are not measured. Attribute data have only two values (conforming/nonconforming, pass/fail, go/no-go, present/absent) but they can be counted, analyzed, and the results plotted to show variation. Measurement can be based on the fraction defective, such as parts per million (PPM). While variables data follows a distribution curve, attribute data varies in steps since you can t count a fraction. There will either be zero errors or a finite number of errors. 

The standard requires appropriate statistical studies to be conducted to anal /ze the variation present in the results of each type of measuring and test equipment system. 

There is considerable evidence to suggest that selenium compounds are anticarcinogens. For one thing, tests with laboratory animals show that the incidence and size of malignant tumors are reduced when a solution containing Na2Se03 is injected at the part per million level. Beyond that evidence, statistical studies show an inverse correlation between selenium levels in the soil and the incidence of certain types of cancer. 

A Statistical study of phenol-formaldehyde resol resin synthesis reaction... 

A two levels of full factorial experimental design with three independent variables were generated with one center point, which was repeated[3]. In this design, F/P molar ratio, Oh/P wt%, and reaction temperature were defined as independent variables, all receiving two values, a high and a low value. A cube like model was formed, with eight comers. One center point (repeated twice) was added to improve accuracy of the design. Every analysis results were treated as a dependent result in the statistical study. 

Baczek, T., Markuszewski, M., Kaliszan, R. Linear and quadratic relationships between retention and organic modifier content in eluent in reversed phase high-performance liquid chromatography a systematic comparative statistical study. 

Statistical studies of MALDI MS applied to bacterial samples show that some biomarker peaks are highly reproducible and appear very consistently, while others appear much less reliably.1719 In Jarman et al.20 and Wahl et al.21 a probability model for MALDI signatures is proposed that takes into account the variability in appearance of biomarker peaks. This method constructs MALDI reference signatures from the set of peak locations for reproducible biomarker peaks, along with a measure of the reproducibility of each peak. 

Pietrogrande, M.C., Marchetti, N., Dondi, F., Righetti, P.G. (2002). Spot overlapping in two-dimensional polyacrylamide gel electrophoresis separations a statistical study of complex protein maps. Electrophoresis 23, 283. 

Pietrogrande, M.C., Dondi, F., Felinger, A., Davis, J.M. (1995). Statistical study of peak overlapping in multicomponent chromatograms importance of the retention pattern. Chemometr. Intell. Lab. Syst. 28, 239. 

In general, for the pad-steam application of basic dyes to acrylic fibres, the auxiliaries are selected to increase the solubility of the dyes with minimal retardation and maximal improvement of fixation. In a detailed statistical study along these lines [60], it was... 

A statistical study of the conversion with tetralin of 68 coals (60) must now be regarded as superseded by a later, more comprehensive paper (61), but it did show very clearly that bivariate plots are of little value in interrelating liquefaction behavior with coal properties at least two or three coal properties must be taken into account in seeking to explain the variance of liquefaction behavior, and some of these properties are not related to the rank of the coal. The paper implies strongly that any interrelationships of coal characteristics must necessarily be multivariate. Hence in any study of coal a large sample and data base is essential if worthwhile generalizations are to be made. 

You may be surprised that for our example data from Miller and Miller ([2], p. 106), the correlation coefficient calculated using any of these methods of computation for the r-value is 0.99887956534852. When we evaluate the correlation computation we see that given a relatively equivalent prediction error represented as (X - X), J2 (X - X), or SEP, the standard deviation of the data set (X) determines the magnitude of the correlation coefficient. This is illustrated using Graphics 59-la and 59-lb. These graphics allow the correlation coefficient to be displayed for any specified Standard error of prediction, also occasionally denoted as the standard error of estimate (SEE). It should be obvious that for any statistical study one must compare the actual computational recipes used to make a calculation, rather than to rely on the more or less non-standard terminology and assume that the computations are what one expected. 

With the number of known exoplanets increasing very fast, current results are giving us the chance to undertake the first statistical studies of the properties of the exoplanets, as well of their host stars [24,21,8]. This is bringing new interesting constraints for the models of planet formation and evolution. 

Gardner [6] has reported a detailed statistical study involving ten laboratories of the determination of cadmium in coastal and estuarine waters by atomic absorption spectrometry. The maximum tolerable error was defined as 0.1 ptg/1 or 20% of sample concentration, whichever is the larger. Many laboratories participating in this work did not achieve the required accuracy for the determination of cadmium in coastal and estuarine water. Failure to meet targets is attributable to both random and systematic errors. 

E. W. Hones, Jr, T. Pytte, and H. I. West, Jr. Associations of Geomagnetic Activity with Plasma Sheet Thinning and Expansion—A Statistical Study, J. Geophy. Res., 89(1984) 5471-5478. 

Knudson AG, Jr. (1971) Mutation and cancer statistical study of retinoblastoma. Proc Natl Acad Sci USA 68 820-823... 

For most astronomers, the solution to these cosmological problems resides in a combination of various methods. The luminosity-redshift test must be combined with independent techniques, such as anisotropies in the cosmic background radiation and statistical study of gravitational lenses. 

Ohmura, R. Ogawa, M. Yasuoka, K. Mori, Y.H. (2003b). Statistical study of clathrate-hydrate nucleation in a water/hydrochlorofluorocarbon system Search for the nature of the "memory effect". J. Phys. Chem. B, 107 (22), 5289-5293. 

It is important for both the clinician and parents to understand the usual natural history of tics. The characteristic temporal pattern of tics is one of short-term bouts or bursts and longer-term waxing and waning. Statistical studies of the temporal dynamics of tics sug-... 

A head of liq expl held in a hollow former provides a flow of expl to compensate for any contraction as solidification occurs) cc) J.G. Holmes, Ordn 42, 193—4 (1957) (Application of single-pour controlled cooling to filling bombs and other expl ordnance) dd) S.D. Stein M.J. Margolin, Proposed Shell Loading Standards Based on a Statistical Study of Setback Sensitivities , PATR 2563 (1958)... 

Statistical Studies. The present suggested standard for air monitoring accuracy is that the absolute total error (sampling and analysis) should be less than 25% in at least 95% of samples analyzed at the level of the standard (1). This implies that the true coefficient of variation of he total error should be no greater than 0.128 derived as follows ... 

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