Errors in Analytical Procedures

ERRORS IN ANALYTICAL PROCEDURES 2.1. Systematic and Random Error 

Errors or uncertainties in the final result is a function of the uncertainties in each step of measurements from planning, sampling, and analysis to reporting. For measurements to be of 

A measurement result is an estimate and may be considered to be without error to measure the correct values, and then the analytical procedures may be considered to be correct or accurate. The accuracy of an analytical procedure and result combines precision and trueness. ISO 5725 [5] defines accuracy as the closeness of agreement between test results and the accepted reference value , and is described by the terms trueness and precision . Trueness refers to the closeness of agreement between the average value of a large number of test results and the true or accepted reference value. Trueness of the analytical procedure is normally measured as a bias. Precision refers to the closeness of agreement between test results. Two measures of precision, termed repeatability and reproducibility, have been established for describing the variability of a measurement method. The first describes the minimum and the second the maximum variability of results, and between these intermediate conditions exist [17]. 

An analytical procedure is in statistical control when the variation among the observed results can be attributed to a constant system of chance causes. It is assumed that an analytical method is in a state of statistical control when the distribution of results can be approximated by the normal distribution around the conventional true value ( Xr) with a standard deviation ( t). When a measurement system is in statistical control the data have statistical predictability and several statistical calculations can be performed for its evaluation and documentation. 

From an ideal point of view, an analytical method should be without any systematic errors, and then the method by definition is in analytical control. A measurement result should be corrected for an estimated systematic error [18], 

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The importance of representative sampling is now recognized the magnitude of errors in analytical procedures was demonstrated for the first time by Fair-bairn et al. (1951) on the basis of a cooperative investigation of chemical and... 

The error in the surface excess is, of course, substantially larger because adsorption levels are quite low and concentration changes due to adsorption are therefore small. An example of uncertainties in the measurements of surface excess for surfactant systems caused by errors in analytical procedures is shown in Figure 7. This error analysis shows clearly that batch methods should not be used for measuring surfactant adsorption on Berea sandstone for surfactant concentrations above 1% unless extremely accurate analytical procedures are developed. 

In actual practice, the concentration of chromate produces an intense yellow colour to such an extent that the end point is masked. Therefore, normally concentrations of 5 x 10 3 M are employed in analytical procedures. It suggests that [Ag+] shall be > 1.3 / 10 5 M at the end-point thereby introducing a positive determinate error. However, it has been proved experimentally that even with concentrations as low as 2 x 10 3 M, the extent of error caused is negligibly small. 

There are several steps that can be taken to ensure accuracy in analytical procedures. Most of these depend on minimizing or correcting errors that might occur in the measurement step. We should note, however, that the overall accuracy and precision of an analysis might be limited not by the measurement step but by factors such as sampling, sample preparation, and calibration, as discussed earlier in this chapter. 

A. This suggests a realistic error envelope of type shown in Fig. 5. Common sense suggests that the reason for this is that the overall errors of analytical procedures are not symmetrical. In many cases it is known experimentally, for instance, that measuring instruments have a larger error at low values and that certain losses are not due to first-order processes but have a zero-order component—that is, a constant, irreducible fraction which becomes proportionately very large with very small quantities. 

The validation of data also is an important step in the process. Validation begins at the station with standard operating procedures for self-consistency of operations and maintenance and with systematic calibration of instruments. Air quality instruments are not particularly reliable so that frequent, careful calibration is required for useful data acquisition. Validation of data is continued after transmission before archiving. To maximize reliability, validation involves a dedicated scientist and engineer whose experience permits identification of possible errors or inconsistencies in reported observations. Finally, the validation process is cross-checked with station performance audits and laboratory intercomparisons to identify discrepancies in analytical procedures. This chain of activity generally makes air quality a rather expensive commodity, a fact that is not appreciated by many users. 

In general uncertainty of measurements comprises many components. Some of these may be estimated on the basis of the statistical distribution of results of series of measurements and are characterized by experimental standard deviations. Estimates of other components can only be based on experience or other information [21]. The uncertainty of measurement is an estimate characterizing the range of values within which the true value of the analyte lies. This is after corrections have been performed for all known systematic errors. For analytical procedures the contributions to uncertainty may be within the following (1) errors estimated from repetitive experiments (2) errors from, e.g., calibration, instmmentation, equipment errors estimated from interlaboratory studies (3) errors from the use of reference materials (reference material uncertainty) (4) sampling errors, etc. 

The 2h fractions present in the water and in the gas absorption duct are then purified as described above and subjected to liquid scintillation counting. The analytical error in this procedure is also on the order of about 6% (standard deviation). 

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. 

Personal Errors Finally, analytical work is always subject to a variety of personal errors, which can include the ability to see a change in the color of an indicator used to signal the end point of a titration biases, such as consistently overestimating or underestimating the value on an instrument s readout scale failing to calibrate glassware and instrumentation and misinterpreting procedural directions. Personal errors can be minimized with proper care. 

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. 

Spike recoveries on method blanks and field blanks are used to evaluate the general performance of an analytical procedure. The concentration of analyte added to the blank should be between 5 and 50 times the method s detection limit. Systematic errors occurring during sampling and transport will result in an unacceptable recovery for the field blank, but not for the method blank. Systematic errors occurring in the laboratory, however, will affect the recoveries for both the field and method blanks. 

An emphasis on critical thinking. Critical thinking is encouraged through problems in which students are asked to explain why certain steps in an analytical procedure are included, or to determine the effect of an experimental error on the results of an analysis. 

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. 

The function of the analyst is to obtain a result as near to the true value as possible by the correct application of the analytical procedure employed. The level of confidence that the analyst may enjoy in his results will be very small unless he has knowledge of the accuracy and precision of the method used as well as being aware of the sources of error which may be introduced. Quantitative analysis is not simply a case of taking a sample, carrying out a single determination and then claiming that the value obtained is irrefutable. It also requires a sound knowledge of the chemistry involved, of the possibilities of interferences from other ions, elements and compounds as well as of the statistical distribution of values. The purpose of this chapter is to explain some of the terms employed and to outline the statistical procedures which may be applied to the analytical results. 

The errors arising in sampling, particularly in the case of heterogeneous solids, may be the most important source of uncertainty in the subsequent analysis of the material. If we represent the standard deviation of the sampling operation (the sampling error) by ss and the standard deviation of the analytical procedures (the analytical error) by sA, then the overall standard deviation sT (the total error) is given by... 

The inherent lability of alkene- and hydroxyalkanesulfonates, variations in isomer composition, and the presence of the disulfonates are features which complicate AOS analyses. Improper sample handling, such as exposure to high temperatures, can also alter active matter composition. Consequently, analytical procedures have been developed that minimize potential sources of error. 

In a widely accepted definition, an analytical method can be defined as the series of procedures from receipt of a sample to the production of the final result. Often, not all procedures can be validated in an adequate way. However, even in such cases, where all procedures of a method are validated, the performance characteristics obtained do not reflect all sources of error. In a recent paper,the complete ladder of errors is described in the following way ... 

The analytical response generated by an immunoassay is caused by the interaction of the analyte with the antibody. Although immunoassays have greater specificity than many other analytical procedures, they are also subject to significant interference problems. Interference is defined as any alteration in the assay signal different from the signal produced by the assay under standard conditions. Specific (cross-reactivity) and nonspecific (matrix) interferences may be major sources of immunoassay error and should be controlled to the greatest extent possible. Because of their different impacts on analyses, different approaches to minimize matrix effects and antibody cross-reactivity will be discussed separately. 

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