Data analytical procedure

The basis of all data-analytical procedures is the data matrix (Eq. 8.10). In many cases the original data x j have to be transformed, either into standardized data ... 

An analytical procedure is often tested on materials of known composition. These materials may be pure substances, standard samples, or materials analyzed by some other more accurate method. Repeated determinations on a known material furnish data for both an estimate of the precision and a test for the presence of a constant error in the results. The standard deviation is found from Equation 12 (with the known composition replacing /x). A calculated value for t (Eq. 14) in excess of the appropriate value in Table 2.27 is interpreted as evidence of the presence of a constant error at the indicated level of significance. 

Let s use a simple example to develop the rationale behind a one-way ANOVA calculation. The data in Table 14.7 show the results obtained by several analysts in determining the purity of a single pharmaceutical preparation of sulfanilamide. Each column in this table lists the results obtained by an individual analyst. For convenience, entries in the table are represented by the symbol where i identifies the analyst and j indicates the replicate number thus 3 5 is the fifth replicate for the third analyst (and is equal to 94.24%). The variability in the results shown in Table 14.7 arises from two sources indeterminate errors associated with the analytical procedure that are experienced equally by all analysts, and systematic or determinate errors introduced by the analysts. 

Hyphenated analytical methods usually give rise to iacreased confidence ia results, eaable the handling of more complex samples, improve detectioa limits, and minimi2e method development time. This approach normally results ia iacreased iastmmeatal complexity and cost, iacreased user sophisticatioa, and the need to handle enormous amounts of data. The analytical chemist must, however, remain cogni2ant of the need to use proper analytical procedures ia sample preparatioas to aid ia improved seasitivity and not rely solely on additional iastmmentation to iacrease detection levels. 

Hyphenated analytical methods provide more complementary information in a shorter time period leading to faster and more reUable results, than data obtained from traditional instmmental methods. The types of analytical instmments that can be joined is very large depending only upon the nondestmction of samples after the initial analytical procedure and the ability of the manufacturer to interface the instmmental techniques. Combinations include separation—separation, separation—identification, and identification—identification techniques (see Analytical methods, survey). 

The simplest analytical procedure is to oxidize a sample in air below the fusion point of the ash. The loss on ignition is reported as graphitic carbon. Refinements are deterrninations of the presence of amorphous carbon by gravity separation with ethylene bromide, or preferably by x-ray diffraction, and carbonates by loss of weight on treating with nitric acid. Corrections for amorphous carbon and carbonates are appHed to the ignition data, but loss of volatile materials and oxidation may introduce errors. 

Using the data in Fig. 4-1, draw the variation in concentration over the 6-hr period as it would appear using sampling and analytical procedures which integrate the concentrations arriving at the receptor over 30 min and 2 hr, respectively,... 

The comparison of the values obtained from a set of results with either (a) the true value or (b) other sets of data makes it possible to determine whether the analytical procedure has been accurate and/or precise, or if it is superior to another method. 

The following are somewhat subjective selections from the vast amount of recent published material on solid proplnts. These short abstracts are grouped under the headings of ignition, combustion, reactivity, detonability safety, analytical procedures data, and miscellaneous. In each grouping the abstracts are arranged chronologically... 

If one is less restrained in setting specification limits, a balance can be struck between customer expectations and the risk and cost of failure a review of available data from production and validation runs will allow confidence limits to be calculated for a variety of scenarios (limits, analytical procedures, associated costs see Fig. 2.15 for an example). 

An alternative for evaluating accuracy is spiking known amounts of standards to a food, as reported in several papers,although percent recoveries of spikes do not truly address the influence of the food matrix complexity on the extraction efficiency. Data evaluation procedures were developed as a manual system to assess the quality of analytical data for carotenoids in foods. ... 

INAA is well suited to study homogeneity of small samples because of its dynamic range of elemental sensitivity. The technique allows for the use of small solid samples, with the smallest usable sample size in the range of 0.5 mg to i mg as determined by handling and blank considerations. The INAA analytical procedure is well understood and characterized with mathematical relationships. Its analytical uncertainties can be sufficiently controlled and can be well determined for a particular procedure. This allows the calculation of the contribution of material heterogeneity to the uncertainty budget based on experimental data. 

Most often studies will be accepted by regulatory authorities even if they do not contain all information. For example, a summary, the scope, a separate notice regarding the residue definition or a schematic diagram of the analytical procedure are helpful and may avoid additional questions, but they are not essential. Also, detailed specification of standard glassware or chemicals commonly used in residue analysis is less important. Finally, data about extraction efficiency or analyte stability can be offered in separate studies or statements, which are also valid for other methods. However, each method must precisely describe at the minimum ... 

In summary, official German analytical methods for pesticide residues are always validated in several laboratories. These inter-laboratory studies avoid the acceptance of methods which cannot readily be reproduced in further laboratories and they do improve the ruggedness of analytical procedures applied. The recently introduced calibration with standards in matrix improves the trueness of the reported recovery data. Other aspects of validation (sample processing, analyte stability, extraction efficiency) are not considered. 

The method using GC/MS with selected ion monitoring (SIM) in the electron ionization (El) mode can determine concentrations of alachlor, acetochlor, and metolachlor and other major corn herbicides in raw and finished surface water and groundwater samples. This GC/MS method eliminates interferences and provides similar sensitivity and superior specificity compared with conventional methods such as GC/ECD or GC/NPD, eliminating the need for a confirmatory method by collection of data on numerous ions simultaneously. If there are interferences with the quantitation ion, a confirmation ion is substituted for quantitation purposes. Deuterated analogs of each analyte may be used as internal standards, which compensate for matrix effects and allow for the correction of losses that occur during the analytical procedure. A known amount of the deuterium-labeled compound, which is an ideal internal standard because its chemical and physical properties are essentially identical with those of the unlabeled compound, is carried through the analytical procedure. SPE is required to concentrate the water samples before analysis to determine concentrations reliably at or below 0.05 qg (ppb) and to recover/extract the various analytes from the water samples into a suitable solvent for GC analysis. 

Third, the bulk of the items in Table 1 address method performance. These requirements must be satisfied on a substrate-by-substrate basis to address substrate-specific interferences. As discussed above, interferences are best dealt with by application of conventional sample preparation techniques use of blank substrate to account for background interferences is not permitted. The analyst must establish a limit of detection (LOD), the lowest standard concentration that yields a signal that can be differentiated from background, and an LOQ (the reader is referred to Brady for a discussion of different techniques used to determine the LOD for immunoassays). For example, analysis of a variety of corn fractions requires the generation of LOD and LOQ data for each fraction. Procedural recoveries must accompany each analytical set and be based on fresh fortification of substrate prior to extraction. Recovery samples serve to confirm that the extraction and cleanup procedures were conducted correctly for all samples in each set of analyses. Carrying control substrate through the analytical procedure is good practice if practicable. 

Before undertaking a discussion of the mathematics involved in the determination of reaction rates is undertaken, it is necessary to point out the importance of proper data acquisition in stability testing. Applications of rate equations and predictions are meaningful only if the data utilized in such processes are collected using valid statistical and analytical procedures. It is beyond the scope of this chapter to discuss the proper statistical treatments and analytical techniques that should be used in a stability study. Some perspectives in these areas can be obtained by reading the comprehensive review by Meites [84], the paper by P. Wessels et al. [85], and the section on statistical considerations in the stability guidelines published by FDA in 1987 [86] and in the more recent Guidance for Industry published in June 1998 [87],... 

The lack of specificity of this biomarker and the complexity of analytical procedures for CS2 determination represent major limitations to the practical use of this metabolite to monitor occupational exposure. Moreover, only few data are available to confirm the validity of CS2 as a biomarker of DTC exposure. 

All solutions of Eqs. (3) such as that by Yu and Sparrow (Yl) yield the velocity profiles in each phase as a function of the interfacial position h and the pressure drop. The volumetric flow rates Qt and Q are obtained by integrating each velocity profile over the respective phase cross-sectional area. The ratio of the flow rates can then be determined as a function of only the interfacial position, and since the volumetric flow rates are known, this yields an implicit fourth order equation for the interfacial position h. The holdups Rt and Rn can be calculated once the interfacial position is known. Since each equation for the volumetric flow rates is linear with respect to the pressure drop, once the interfacial position is known the pressure drop may be easily computed. An analytical procedure for determining pressure drop and holdup for turbulent gas-laminar liquid flows has been developed by Etchells (El) and verified by comparison with experimental data in horizontal systems (A7). 

Perhaps the most discouraging type of deviation from linearity is random scatter of the data points. Such results indicate that something is seriously wrong with the experiment. The method of analysis may be at fault or the reaction may not be following the expected stoichiometry. Side reactions may be interfering with the analytical procedures used to follow the progress of the reaction, or they may render the mathematical analysis employed invalid. When such plots are obtained, it is wise to reevaluate the entire experimental procedure and the method used to evaluate the data before carrying out additional experiments in the laboratory. 

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