Statistics correlation

EmpiricalEfficieny Prediction Methods. Numerous empirical methods for predicting plate efficiency have been proposed. Probably the most widely used method correlates overall column efficiency as a function of feed viscosity and relative volatiHty (64). A statistical correlation of efficiency and system variables has been developed from numerous plate efficiency data (65). 

Timoshenko et al (1967) recommended running a set of experiments in a CSTR on feed composition (now called feed-forward study), and then statistically correlating the discharge concentrations and rates with feed conditions by second order polynomials. In the second stage, mathematical experiments are executed on the previous empirical correlation to find the form and constants for the rate expressions. An example is presented for the dehydrogenation of butane. 

It is important to keep in mind that statistically based studies by themselves can never prove the e.xistence of a cause and effect relationship. However, such obseix ations may be used to generate or to test a hypothesis. Many possibilities exist for introducing bias in this type of investigation, and statistical correlations may be fortuitous. 

Hall and Mudawar (2000) provided a comprehensive review of the current state of the knowledge of subcooled CHF for water flow boiling in channels, and designed a statistical correlation with five parameters based on almost all available subcooled CHF databases in the literature ... 

Trends Seasonal variations Basic statistics Correlation... 

Moin, R. and J. Kim, The structure of the vorticity field in turbulent channel flow. Rart 1. Analysis of instantaneous fields and statistical correlations. /. Fluid Mech., 1985.155 441 4. 

In most studies, phytoestrogen intake has been estimated by direct methods that evaluate food intake either by recall (food-frequency questionnaires -FFQs) or by record (food diary), and subsequently by composition databases based on information of this kind. Food-frequency questionnaires are widely administered to subjects involved in epidemiological studies. Their validity and reproducibility is considered sufficient when statistically correlated to data obtained from dietary records (a properly-completed and comprehensive food diary) and from analysis of blood and urine samples (Kirk et ah, 1999 Huang et al, 2000 Yamamoto et al, 2001 Verkasalo et al, 2001). FFQs can be repeated several times a year and may be administered to large populations. Such an approach provides an easy and low-cost method of assessing the... 

LEED patterns at 0 = 1 /4, but was identified at lower coverages in islands surrounded by mobile sulfur atoms at platinum, rhodium and rhenium surfaces. Sautet and co-workers42 have analysed the statistical correlations between the intensities of sulfur features in p(2 x 2) islands on rhenium surfaces and also of streaks in areas between islands, which they attribute to sulfur atoms diffusing under the tip (Figure 10.12). 

Table 5.9 summarises the main features of FTIR spectroscopy as applied to extracts (separated or not). Since many additives have quite different absorbance profiles FTIR is an excellent tool for recognition. Qualitative identification is relatively straightforward for the different classes of additives. Library searching entails a sequential, point-by-point, statistical correlation analysis of the unknown spectrum with each of the spectra in the library. Fully automated analysis of... 

Software sensors and related methods - This last group is considered because of the complexity of wastewater composition and of treatment process control. As all relevant parameters are not directly measurable, as will be seen hereafter, the use of more or less complex mathematical models for the calculation (estimation) of some of them is sometimes proposed. Software sensing is thus based on methods that allow calculation of the value of a parameter from the measurement of one or more other parameters, the measurement principle of which is completely different from an existing standard/reference method, or has no direct relation. Statistical correlative methods can also be considered in this group. Some examples will be presented in the following section. 

It is not entirely clear whether the acetone co-exposure in the Sanagi et al. (1980) study contributed to the observed effects. Indirect evidence from an occupational study (Cardona et al. 1996) showed that workplace acetone concentrations had a statistical correlation with the ratio of urinary -hexane metabolites to /i-hcxanc air concentration, although it did not correlate with measured urinary metabolites. No animal studies are available describing the effects of inhalation co-exposure to acetone and -hexane, although there are several studies which report interactions between acetone and the neurotoxic metabolite of -hexane 2,5-hexanedione (See Section 2.4, Mechanisms of Action). Oral administration of acetone has been reported to potentiate the neurotoxicity caused by oral exposure to the neurotoxic u-hexane metabolite 2,5-hexanedione in rats (Ladefoged et al. 1989, 1994). Oral exposure to acetone alone in rats at 650 mg/kg/day resulted in a statistically significant decrease in motor nerve conduction velocity after 6 weeks co-exposure to acetone and 2,5-hexanedione resulted in greater effects... 

Since the comparison of rxy with the table values may be considered a somewhat weak test, it is perhaps more meaningful to compare the tr value with values in a t-distribution table for N-2 degrees of freedom (df), as is done for Student s I-tcst. This will give a more exact determination of the degree of statistical correlation between the two groups. 

In a very broad overview of the structural categories one can state several statistical correlations with type of function. Hemes are almost always bound by helices, but never in parallel a//3 structures. Relatively complex enzymatic functions, especially those involving allosteric control, are occasionally antiparallel /3 but most often parallel a//3. Binding and receptor proteins are most often antiparallel /3, while the proteins that bind in those receptor sites (i.e., hormones, toxins, and enzyme inhibitors) are most apt to be small disulfide-rich structures. However, there are exceptions to all of the above generalizations (such as cytochrome cs as a nonhelical heme protein or citrate synthase as a helical enzyme), and when one focuses on the really significant level of detail within the active site then the correlation with overall tertiary structure disappears altogether. For almost all of the dozen identifiable groups of functionally similar proteins that are represented by at least two known protein structures, there are at least... 

Fig. 1. Auto-correlation function of the energy and the best fit for a double exponential decay used to obtain the interval of statistical correlation.

The research was greatly facilitated by two important elements. The (formal, perturbative) solution of the Liouville equation is greatly simplified by a Fourier representation (see Appendix). The latter allows one to easily identify the various types of statistical correlations between the particles. The traditional dynamics thus becomes a dynamics of correlations. The latter is completed by... 

Abdul, S.A., Gibson, T.L., and Rai, D.N. Statistical correlations for predicting the partition coefficient for nonpolar organic contaminants between aquifer organic carbon and water, Haz. Waste Haz. Mater., 4(3) 211-222, 1987. 

There is no statistical correlation between good grades and success in life. For most of us, our performance in school was a major... 

A more common use of informatics for data analysis is the development of (quantitative) structure-property relationships (QSPR) for the prediction of materials properties and thus ultimately the design of polymers. Quantitative structure-property relationships are multivariate statistical correlations between the property of a polymer and a number of variables, which are either physical properties themselves or descriptors, which hold information about a polymer in a more abstract way. The simplest QSPR models are usually linear regression-type models but complex neural networks and numerous other machine-learning techniques have also been used. 

Erythrocytic effect. Hydrogenated coconut oil, administered orally to healthy rats for 10 weeks, produced a significant effect on five of the six classes of erythrocytes identified. The proportion of cells in each class was dependent on the diet. There was no significant effect of diet on erythrocyte filterability index and no statistical correlation between erythrocyte filterability index and morphology " . 

The basic concept of microdosimetry is the microdosimetric event (or, simply, event), which is energy deposition by a charged particle and its statistically correlated particles (e.g., secondary electrons from the same particle track) [15-17]. Events are important because they are statistically independent entities. The principal microdosimetric quantity, specific energy z, is defined as follows ... 

Public concern about industrial chemical exposures might also be misguided. The EPA typically uses mathematical dispersion models to calculate human exposure to chemicals released into the air by major stationary sources like factories and power plants. There is little evidence that the models are predictive. In one experiment, a tracer gas was released from the Alaska pipeline terminus at Valdez. Actual exposure, as measured by personal exposure badges, was compared with the predictions of the EPA dispersion model. The statistical correlation between them was near zero (— 0.01), meaning the predictions were worthless (Wallace 1993, 137-38). 

Analysis of trends in transition metal chemical shifts was in most cases attempted by exploring statistical correlations with other observable spectroscopic quantities such as ligand atom chemical shifts or metal-ligand coupling constants... 

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