Precision difference method

Blatz [ ] developed a precise difference, method for the spec-trophotometric determination of cerium (IV) at micromolar concentrations. He studied such variables as suspended material, presence of organic (reducing) materials, purification of reagents and solutions, cell constants, stray light, interferences, optimum reagent concentrations, time factors, and blanks, finally achieving a probable error of 0.25% (I favor the school that deems the probable error to be neither probable nor an error and prefer to think of this as a standard deviation of 0.37%). 

Blatz [ ] devised a precise difference method for cerium to which we have already alluded. Ultraviolet methods include measuring in carbonate solution dilute sulfuric acid at 315 m/tt 320 m/i... 

The precise geometrical data obtained by microwave spectroscopy allow conclusions regarding bond delocalization and hence aromaticity. For example, the microwave spectrum of thiazole has shown that the structure is very close to the average of the structures of thiophene and 1,3,4-thiadiazole, which indicates a similar trend in aromaticity. However, different methods have frequently given inconsistent results. 

The comparison of the results of very different methods has to be judged very precisely, as, e.g., the given thickness of a layer is a function of the limit of detection (EOD) of a method. Additionally, the detected areas vary from about 0.01 up to about 400 mm-. Therefore, the methods with a low level of detection and with a high sensitivity (high slope of the calibration function) give a higher value for the layer thickness. Furthermore, the layers are broadened with time by diffusion. 

Many numerical methods have been proposed for this problem, most of them finite-difference methods. Using a finite-difference technique, Brode (1955) analyzed the expansion of hot and cold air spheres with pressures of 2000 bar and 1210 bar. The detailed results allowed Brode to describe precisely the shock formation process and to explain the occurrence of a second shock. 

The relative error is the absolute error divided by the true value it is usually expressed in terms of percentage or in parts per thousand. The true or absolute value of a quantity cannot be established experimentally, so that the observed result must be compared with the most probable value. With pure substances the quantity will ultimately depend upon the relative atomic mass of the constituent elements. Determinations of the relative atomic mass have been made with the utmost care, and the accuracy obtained usually far exceeds that attained in ordinary quantitative analysis the analyst must accordingly accept their reliability. With natural or industrial products, we must accept provisionally the results obtained by analysts of repute using carefully tested methods. If several analysts determine the same constituent in the same sample by different methods, the most probable value, which is usually the average, can be deduced from their results. In both cases, the establishment of the most probable value involves the application of statistical methods and the concept of precision. 

The choice of the method is governed by what is suitable for the given species (reactants or products), by the availability of instrumentation, and by the experience and familiarity of the investigator with the different methods. As mentioned, the time scale of the reaction must be compatible with the analytical method, and its response, precision, and sensitivity must be appropriate for the concentrations chosen. Generally speaking, it is best to select a method that can provide concentrations to a precision of at least 1-2%. 

A.23 The density of a metal was measured by two different methods. In each case, calculate the density. Indicate which measurement is more precise, (a) The dimensions of a rectangular block of the metal were measured as 1.10 cm X 0.531 cm X 0.212 cm. Its mass was found to be 0.213 g. (b) The mass of a cylinder of water filled to the 19.65-mL mark was found to be 39.753 g. When a piece of the metal was immersed in the water, the level of the water rose to 20.37 ml. and the mass of the cylinder with the metal was found to be 41.003 g. 

The molecular weight of transferrin is not known precisely. Different modern methods have yielded weights ranging from 68,000 to 89,000 (Katz, 1970). 

The evidence presented fails to suggest the causes for the large variations in crystallinity estimates which have been reported for similar cellulosic materials. There is a possibility that the different methods may not measure precisely the same characteristic of the material. It also may be that relative crystallinity is not a fixed quantity in any case but depends on circumstances involved in the measurement, such as the amount of swelling. The estimates reached by different methods need to be reconciled. At present, crystallinity estimates which depend wholly or in part on X-ray diffraction seem to be much higher than those obtained by chemical methods. The fact is that X-ray diffraction methods are ideal for studies of the crystalline fraction but are necessarily indirect in application to the non-crystalline fraction. The converse is true for the chemical approach. Apparently a combination of diffraction and chemical methods may adjust the existing differences. 

In contrast to many chemotherapeutic agents in cancer therapy, boron compounds for BNCT do not require a tumoricidal action in their own right. For their successful application in the therapy of patients, it is important to deliver, to the tumor, a radiation dose which is higher than the radiation dose to the surrounding tissue. The demonstration that this is actually achieved lies ultimately in the treatment of the tumor in question. Because of the short range of the particles produced in the 10B(n,a)7Li reaction, it is very important where, on a cellular and subcellular dimension, the neutron capture reaction takes place. Different methods for boron detection and quantification give different resolution of the boron distribution. It is instructive to compare these methods, both for their precision and lower detection limits, as well as for their ability to yield an image of the boron distribution in tissue (Table 2.2-1). 

The relatively small mass differences for most of the elements discussed in this volume requires very high-precision analytical methods, and these are reviewed in Chapter 4 by Albarede and Beard (2004), where it is shown that precisions of 0.05 to 0.2 per mil (%o) are attainable for many isotopic systems. Isotopic analysis may be done using a variety of mass spectrometers, including so-called gas source and solid source mass spectrometers (also referred to as isotope ratio and thermal ionization mass spectrometers, respectively), and, importantly, MC-ICP-MS. Future advancements in instrumentation will include improvement in in situ isotopic analyses using ion microprobes (secondary ion mass spectrometry). Even a small increase in precision is likely to be critical for isotopic analysis of the intermediate- to high-mass elements where, for example, an increase in precision from 0.2 to 0.05%o could result in an increase in signal to noise ratio from 10 to 40. 

It is critical when performing quantitative GC/MS procedures that appropriate internal standards are employed to account for variations in extraction efficiency, derivatization, injection volume, and matrix effects. For isotope dilution (ID) GC/MS analyses, it is crucial to select an appropriate internal standard. Ideally, the internal standard should have the same physical and chemical properties as the analyte of interest, but will be separated by mass. The best internal standards are nonradioactive stable isotopic analogs of the compounds of interest, differing by at least 3, and preferably by 4 or 5, atomic mass units. The only property that distinguishes the analyte from the internal standard in ID is a very small difference in mass, which is readily discerned by the mass spectrometer. Isotopic dilution procedures are among the most accurate and precise quantitative methods available to analytical chemists. It cannot be emphasized too strongly that internal standards of the same basic structure compensate for matrix effects in MS. Therefore, in the ID method, there is an absolute reference (i.e., the response factors of the analyte and the internal standard are considered to be identical Pickup and McPherson, 1976). 

Intermediate precision is another measure of the performance of the method where samples are tested and compared using different analysts, different equipment, different days, etc. This study is a measure of interlab variability and is a measure of the precision that can be expected within a laboratory. Intermediate precision is not required if a reproducibility study has been performed. Table 6 lists the ranges and suggested acceptance criteria for evaluation of precision during method development. 

Another possibility is to choose expert laboratories, which are able to measnre with high precision reference methods, ntilising traceable calibration materials. If these laboratories use methods based on different physieo-chemical principles and eome to more or less the same result, it is very probable that the value is elose to the true value. 

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