Precision estimates, comparison

A fully parametric model/estimator provides consistent, efficient, and comparatively precise results. The semiparametric model/estimator, by comparison, is relatively less precise in general terms. But, the payoff to this imprecision is that the semiparametric formulation is more likely to be robust to failures of the assumptions of the parametric model. Consider, for example, the binary probit model of Chapter 21, which makes a strong assumption of normality and homoscedasticity. If the assumptions are coirect, the probit estimator is the most efficient use of the data. However, if the normality assumption or the homoscedasticity assumption are incorrect, then the probit estimator becomes inconsistent in an unknown fashion. Lewbel s semiparametric estimator for the binary choice model, in contrast, is not very precise in comparison to the probit model. But, it will remain consistent if the normality assumption is violated, and it is even robust to certain kinds of heteroscedasticity. 

The extrapolation of animal toxicology data and combination with human exposure data aiay be used to estimate risk for those situations where exposure is likely. Methods for integrating these data as well as the assumptions for extrapolation from the animal studies are dependent upon the safety data. Risk assessment includes consideration of the type of toxicity involved and its potency, species comparisons, time considerations, dose response, kinetics of homeostatic mechanisms, and mechanisms of toxicity. When the essential components for extrapolations are well understood, more precise estimates can be made. In the absence of such understanding, more conservative approaches are appropriate. 

Precision is the closeness of agreement between independent test results obtained under stipulated conditions. Repeatability is the precision estimated by a single analyst using a given equipment over a short time scale. Reproducibility is the precision estimated by elaborating the results obtained by a number of laboratories (for example in among-laboratories comparison). A third type of precision is sometimes known as intermediate precision. In this last case, it is estimated in a single laboratory but by different analysts, or over extended time scales. 

K Fe(CN)6 oxidation Compound F is stoichiometrically inactivated by oxidation with K.3Fe(CN)6 (Shimomura and Johnson, 1967) thus, it is possible to estimate the molecular extinction coefficient (e) of the 388-390 nm absorption peak by titrating F with K.3Fe(CN)6- The e value obtained by the titration in 50% ethanol was 15,400 (assuming the reaction to be one-electron oxidation) or 30,800 (assuming two-electron oxidation). Two other methods of lesser precision were used to determine the true s value 1) the dry weight of the ethyl acetate extract of an acidified solution of F gave an e value of 14,100 2) the comparison of NMR signal intensities gave a value of 11,400 2,000 in water (H. Nakamura, Y. Oba, and A. Murai, 1995, personal... 

The values of x in column 4 were obtained by the Ethyl Corporation by a chemical method, for which the estimated precision is 0.02 ml of tetraethyllead fluid per gallon. Comparison of columns 4 and 5 shows agreement within these limits for all samples except B62M-3 the reason for the considerably greater discrepancy here is unknown. The precision of the x-ray work is better than was expected. (The precision is sufficiently great to warrant consideration of the difference in the x-ray absorption of the base stocks, samples AOT-1 and B62M-1.) Further-... 

The semiempirical methods represent a real alternative for this research. Aside from the limitation to the treatment of only special groups of electrons (e.g. n- or valence electrons), the neglect of numerous integrals above all leads to a drastic reduction of computer time in comparison with ab initio calculations. In an attempt to compensate for the inaccuracies by the neglects, parametrization of the methods is used. Meaning that values of special integrals are estimated or calibrated semiempirically with the help of experimental results. The usefulness of a set of parameters can be estimated by the theoretical reproduction of special properties of reference molecules obtained experimentally. Each of the numerous semiempirical methods has its own set of parameters because there is not an universial set to calculate all properties of molecules with exact precision. The parametrization of a method is always conformed to a special problem. This explains the multiplicity of semiempirical methods. 

Validate routine methods, i.e., define the conditions under which the assay results are meaningful.115 To do that, one must select samples that are truly representative of the product stream. This may be a difficult task when the process is still under development and the product stream variable. The linearity of detector response should be defined over a range much broader than that expected to be encountered. Interference from the sample matrix and bias from analyte loss in preparation or separation often can be inferred from studies of linearity. Explicit detection or quantitation limits should be established. The precision (run-to-run repeatability) and accuracy (comparison with known standards) can be estimated with standards. Sample stability should be explored and storage conditions defined. 

The analytical results for each sample can again be pooled into a table of precision and accuracy estimates for all values reported for any individual sample. The pooled results for Tables 34-7 and 34-8 are calculated using equations 34-1 and 34-2 where precision is the root mean square deviation of all replicate analyses for any particular sample, and where accuracy is determined as the root mean square deviation between individual results and the Grand Mean of all the individual sample results (Table 34-7) or as the root mean square deviation between individual results and the True (Spiked) value for all the individual sample results (Table 34-8). The use of spiked samples allows a better comparison of precision to accuracy, as the spiked samples include the effects of systematic errors, whereas use of the Grand Mean averages the systematic errors across methods and shifts the apparent true value to include the systematic error. Table 34-8 yields a better estimate of the true precision and accuracy for the methods tested. 

This set of articles presents the computational details and actual values for each of the statistical methods shown for collaborative tests. These methods include the use of precision and estimated accuracy comparisons, ANOVA tests, Student s t-testing, The Rank Test for Method Comparison, and the Efficient Comparison of Methods tests. From using these statistical tests the following conclusions can be derived ... 

Gill and Fitzgerald [481] determined picomolar quantities of mercury in seawater using stannous chloride reduction and two-stage amalgamation with gas-phase detection. The gas flow system used two gold-coated bead columns (the collection and the analytical columns) to transfer mercury into the gas cell of an atomic absorption spectrometer. By careful control and estimation of the blank, a detection limit of 0.21 pM was achieved using 21 of seawater. The accuracy and precision of this method were checked by comparison with aqueous laboratory and National Bureau of Standards (NBS) reference materials spiked into acidified natural water samples at picomolar levels. Further studies showed that at least 88% of mercury in open ocean and coastal seawater consisted of labile species which could be reduced by stannous chloride under acidic conditions. 

Choice of Potential Bioavailability Criterion. It is usually assumed that calcium must be soluble and probably ionized in order to be available for absorption ( ). For the in vitro procedure, as a first approximation we chose calcium solubility after centrifugation at 18,000 x g as the measure of potential bioavailability (Figure 1). We assumed that this would probably overestimate the available calcium and later work based on fractionation might define the bioavailable calcium more precisely. The data in Table IV illustrate how the choice of criterion for "solubility" could affect the in vitro estimate of potential availability, even if in vitro conditions closely resembled in vivo conditions. Since our in vitro criterion unexpectedly underestimated calcium bioavailability for two of the three foods in the direct in vivo - in vitro comparison (8), it was necessary to determine the in vitro digestion conditions which might be limiting solubility before addressing the choice of appropriate criterion. 

Most of the forementioned studies which examined the influence of various dietary fiber on the bioavailability of calcium by human subjects have depended upon the comparative measurements of calcium content of diets and calcium contents of stools and urine. As reviewed by Allen (3), calcium balance studies have distinct limitations relative to accuracy and precision. However, their ease of application and cost, laboratory equipment requirements, and real (or perceived) safety in comparison to available radioactive or stable isotope methods continue to make their use popular. In calcium balance studies, calcium absorption is assumed to be the difference between calcium excretion in the feces and calcium intake. Usually this is expressed as a percent of the calcium intake. This method assumes that all fecal calcium loss is unabsorbed dietary calcium which is, of course, untrue since appreciable amounts of calcium from the body are lost via the intestinal route through the biliary tract. Hence, calcium absorption by this method may underestimate absorption of dietary calcium but is useful for comparative purposes. It has been estimated that bile salts may contribute about 100 g calcium/day to the intestinal calcium contents. Bile salt calcium has been found to be more efficiently absorbed through the intestinal mucosa than is dietary calcium (20) but less so by other investigators (21). 

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