Test parameters, correlation

The main concept addressed in this new multi-part series is the idea of correlation. Correlation may be referred to as the apparent degree of relationship between variables. The term apparent is used because there is no true inference of cause-and-effect when two variables are highly correlated. One may assume that cause-and-effect exists, but this assumption cannot be validated using correlation alone as the test criteria. Correlation has often been referred to as a statistical parameter seeking to define how well a linear or other fitting function describes the relationship between variables however, two variables may be highly correlated under a specific set of test conditions, and not correlated under a different set of experimental conditions. In this case the correlation is conditional and so also is the cause-and-effect phenomenon. If two variables are always perfectly correlated under a variety of conditions, one may have a basis for cause-and-effect, and such a basic relationship permits a well-defined mathematical description. 

Lactic acid fermentation was the topic of a paper by Vaccari et al.35 In this work, lactic acid, glucose, and biomass were determined over the course of the reaction. The measurements were made in real time, using a bypass pump and flow-through cell for the NIR measurements. Instead of using normal chemomet-ric statistics, the authors used correlation coefficients, mean of differences, standard deviation, student s t-test, and the student test parameter of significant difference to evaluate the results. Under these restrictions, the results appeared fairly good, with the biomass having the best set of statistics. 

Pressure-drop data obtained in these tests were correlated empirically by defining a friction-factor based on gas-phase properties and superficial gas-flow rates. This friction-factor was plotted against the group Glijll/Ggi G with the water-oil feed mass-ratio as a parameter. 

When tested in correlations, the MSD parameter offered rather modest results (one should consult Ref.16a> and the literature cited there in). Quite possibly, these results can be justified by the fact that a single number steric parameter does not... 

Visky, D., Y. Vander Heyden, T. Ivanyi, et al. 2002. Characterisation of reversed-phase liquid chromatographic columns by chromatographic tests. Evaluation of 36 test parameters Repeatability, reproducibility and correlation. J. Chromatogr. A 977 39-58. 

Correlations were also established between UL 94, LOI, MCC, and cone calorimetry for both halogenated and nonhalogenated FR wire and cable compounds.149 The study (Figure 26.5) indicated that LOI has poor correlation with MCC parameters due to different flame combustion mechanisms in the LOI (incomplete combustion) and the MCC (forced complete combustion) tests. This correlation was improved by taking into account the burning efficiencies (i.e., combustion and heat transfer efficiencies) of the polymer compounds.150... 

FAST (Fabric Assurance by Simple Testing) is another well known system. It was developed for quality assessment in the wool garment industry. FAST is less expensive and much quicker than the KES-F because it measures only some aspects of the fabric hand such as compression, bending, extension and dimensional stability at a few given points in a simplified form. The first three parameters correlate fairly well with the perceived softness but no quantitative hand values are calculated. For the evaluation of yam softness, there are several other devices in use, for example the p-Meter (Zweigle), a frictional balance (Reibwertwaage from Schlafhorst) and the F-meter. 

In characterizing hypnograms using the nonlinear mixed effects modeling approach, it is important to test for correlations between r values of one transition model and those from another model using individual estimates of r values. Correlations detected should be accounted for in the model. Correlations with correlation coefficient (r) > 0.75 are termed high correlations and correlations with r values between 0.5 and 0.75 are moderate correlations (25). Not accounting for such correlations may yield parameter estimates with poor precision. 

Cheng (Cl) in collaboration with National Research Corporation was the first to carry out exhaustive experimental tests for correlating pressure drop under high vacuum with such parameters as pipe length, pipe diameter, mean gas pressure, and gas throughput. The range of pressures in-... 

In our last experiment (Hampl et al, submitted for publication), we tested the short-term effect of controlled soy consumption on major laboratory thyroid parameters. In contrast to the intervention studies, reviewed above, lasting from 4 weeks to 2 years, the subjects ate soy-rich food only for 1 week. As in the previous study, one of the major tasks was to investigate whether thyroid parameters correlate with actual free isoflavone levels. 

The recoil chemistry of tritium is perhaps one of the best understood in terms of a clear idea of the product spectrum under various conditions. Realistic models have been tested and correlations with theoretical approaches have been made. Thermal-neutron absorption reactions of lithium-6 and helium-3 have been used to produce hot tritium atoms. Some physical parameters are listed in Table 2. 

Abraham and Le (1999) compared many methods for the description, estimation, and prediction of the aqueous solubility of diverse compounds, some methods involving a training set and a subsequent test set of solutes. Standard deviations of the multi-parameter correlations of log s were generally not smaller than 0.5 (a factor of 3 in the solubility ). They then reverted to an LSER-type expression ... 

The results were found to be sensitive to the choice of force field and atomic partial charges used in the simulations, but for the best tested parameters a reasonable correlation between experimental and computed amorphous solubilities was observed [40, 41]. It was shown in Ref. [41] that after reparameterization of the model and introducing an empirical relationship through linear regression analysis of experimental and calculated data = 2.04AG p), amorphous solubility could be... 

Having identified pairs of correlated variables, two problems remain in deciding which one of a pair to eliminate. First, is the correlation real , in other words has the high correlation coeSicient arisen due to a true correlation between the variables or is it caused by some point and cluster effect (see Section 6.2) due to an outlier. The best, and perhaps simplest, way to test the correlation is to plot the two variables against one another, effects due to outliers will then be apparent. It is also worth considering whether the two parameters are likely to be correlated with one another. If one is electronic and the other steric then there is no reason to expect a correlation, although one may exist, of course. On the other hand, maximum width and molecular weight may well be correlated for a set of molecules with similar overall shape. 

Wienand et al. (1982) to propose and to test the correlations between the energy distance A = E(Xi)-E (Fv) and the phenomenological covalency parameter of the host lattice, as defined by Hannay and Smyth (1946) ... 

Both Fig. 11 and Fig. 12 could lead to the conclusion that it is rather hopeless to predict the entrainment from fluidized beds with a reasonable degree of accuracy. However, we see also that a group of correlations is not too far away from the experimental results. In a given situation one should always carefully select one or more correlations, which have been developed on a data basis, which includes the situation under consideration. For example, one should certainly not expect a correlation developed for fine particle systems to hold for a coarse particle system. The gas velocity, the type of solids, and particularly the particle size distribution should be for a given application within the range of tested parameters of the selected correlation. In any case, the results of such correlations should be treated with care an uncertainty of plus/minus 100% should be taken into account. 

In brief, the reason that NQI parameters are so useful is because the tenets of molecular structure and reactivity that are used to describe chemistry are based on models that describe an arrangement of atoms subject to character in the sense that some constituents are charged, neutral, or in some way polarized. For example, chlorine-containing molecules are useful subjects for testing the correlation between nuclear quadrupole interaction parameters and bond properties because both extremes of bond character are easily measured a purely ionic character assigned to chlorine would yield a nearly complete shell associated with chlorine and no nuclear quadrupole coupling, whereas a covalent bond, such as that of CI2, would... 

Fouling propensity is commonly assessed by monitoring permeate flux and transmembrane pressure (TMP). Since membrane processes are generally operated either under constant TMP or constant permeate flux, a decrease in permeate flow rate or an increase of TMP is observed, respectively, once the fouling forms on the membrane. From these two parameters, calculation of hydraulic resistance (m ), membrane permeability (Lm h bar ) or specific cake resistance (mkg ) is also possible and allows further assessment of fouling conditions. The hydraulic resistance of the filtration system can be quantified by correlating TMP and permeate flux during a clean water test. This correlation is described as the Darcy s law ... 

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