Analytical results, accuracy

Two basic parameters should be considered when discussing analytical results accuracy ( absence of systematic errors ) and uncertainty (coefficient of variation or confidence interval) caused by random errors and random variations in the procedure. In this context, accuracy is of primary importance. However, if the uncertainty in a result is too high, it cannot be used for any conclusion concerning, for example, the quality of the environment or of food. An unacceptably high uncertainty renders the result useless. 

Every analytical result forms the basis for a subsequent decision process. So the result should be subject to a high degree of precision and accuracy. This is also true of chromatographic methods. The physical detection methods described until now are frequently not sufficient on their own. If this is the case they have to be complemented by specific chemical reactions (derivatization). 

The difference between the most probable analytical result and the true value for the sample is termed the systematic error in the analysis it indicates the accuracy of the analysis. 

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. 

Standard addition. A known amount of the constituent being determined is added to the sample, which is then analysed for the total amount of constituent present. The difference between the analytical results for samples with and without the added constituent gives the recovery of the amount of added constituent. If the recovery is satisfactory our confidence in the accuracy of the procedure is enhanced. The method is usually applied to physico-chemical procedures such as polarography and spectrophotometry. 

Figure 10-1 illustrates two statements that experience has shown to be generally valid for analytical results obtained by wet methods (1) The true value a and the mean x are different quantities, and one cannot be predicted from the other. (2) No conclusions about the frequency distribution can be drawn from a or from x. One more generalization applies to comparative x-ray methods, be they absorption (3.10) or emission (7.8) methods If the comparison is properly carried out, questions of accuracy will never arise properly includes the use of a... 

In several chapters we discussed how the quality of the analytical result defines the amount of information which is obtained on a sampled system. Obvious quality criteria are accuracy and precision. An equally important criterion is the analysis time. This is particularly true when dynamic systems are analyzed. For instance a relationship exists between the measurability and the sampling rate, analysis time and precision (see Chapter 20). The monitoring of environmental and chemical processes are typical examples where the management of the analysis time is... 

This development has taken place remarkably quickly over the past thirty years. In that period the first attempts to arrive at a proven analytical accuracy were made. Those who led the move were often considered as people with hobbies, obsessive even. Some eye-opening publications demonstrated clearly that generating analytical results could be compared with the generation of numbers in a lottery (G. Tolg), but were received skeptically by the scientific establishment. Even as recently as the late 1970 s even the most highly respected universities still had to be made aware that a result was not necessarily an accurate result. 

A combination of techniques is typically used to verify the accuracy and precision of agrochemical applications to soil. For example, the catch-back method or passtime method is typically used in conjunction with analytical results from application verification monitors to confirm proper application. The catch-back method involves measuring the spray solution volume before and after application to double check that the desired volume of test solution was actually applied to the test plots. Experienced applicators are often able to apply within 2% of the targeted spray volume. 

Accuracy. In general, the accuracy of analytical results is assured by recovery studies (Wegscheider [1996] Danzer [1995] Burns et al. [2002]). According to the recovery function in the general three-dimensional calibration model (see Fig. 6.3), common studies on systematic deviations (Fig. 4.3), and Eqs. (4.2) and (4.3) the following recovery formulae... 

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. 

CALCULATING THE NUMBER OF MEASUREMENTS REQUIRED TO ESTABLISH A MEAN VALUE (OR ANALYTICAL RESULT) WITH A PRESCRIBED UNCERTAINTY (ACCURACY)... 

If error is random and follows probabilistic (normally distributed) variance phenomena, we must be able to make additional measurements to reduce the measurement noise or variability. This is certainly true in the real world to some extent. Most of us having some basic statistical training will recall the concept of calculating the number of measurements required to establish a mean value (or analytical result) with a prescribed accuracy. For this calculation one would designate the allowable error (e), and a probability (or risk) that a measured value (m) would be different by an amount (d). 

Alford Stevens et al. [49] carried out a multi-laboratory study of automated gas chromatography-mass spectrometric determinations of polychlorinated biphenyls in soil. The influence of various factors on the accuracy of analytical results were studied. Shaker extraction for 12.5h followed by Florisil chromatography were demonstrated to be the most reliable methods for extraction and clean-up. 

Obviously, the technology exists for obtaining analytical results without special preparation and analysis in a laboratory. However, at the present time there is no acceptable substitute for direct laboratory examination of samples if we want the kind of accuracy and confidence we have come to expect. All conventional methods for analysis of solid materials require one or more of the following preparation activities before an analytical method can be properly executed 1) particle size reduction, 2) homogenization and division, 3) partial dissolution, and 4) total dissolution. Let us briefly discuss each of these individually. 

In the new Stratus CS system results are available in less than 15 min after sample draw and the system has the capability to analyze four samples in less than 30 min. Ease of use, analytical sensitivity, accuracy, precision, and reproducibility makes this system suitable for use in chest pain centers, emergency departments, critical care units, observation wards and clinical laboratories. 

To collect a representative sample forms a vital aspect of analytical chemistry, because the samples subjected to analysis are assumed to be perfectly homogeneous and truly representative. Thus, sampling may be considered as the most critical aspect of analysis. In other words, the accuracy and significance of measurements may be solely limited by the sampling process. Unless and until the sampling process is performed properly, it may give rise to a possible weak link in the interpretation of the analytical results. For instance, the improper... 

Mandel, J. Accuracy andPrecision Evaluation and Interpretation of Analytical Results , InTreatise on Analytical Chemistry, ed. by I.M Kolthoff and PJ. Elving, 2nd edn., Vol. 1. New York, Wiley and Sons, Inc., 1978. 

The need for reporting accuracy and error in the form of confidence limits when reporting analytical results has already been well outlined ( ). The confidence interval requires... 

To determine the QL, it is necessary to agree on acceptable limits for precision and accuracy. Commonly, precision is given as a maximal acceptable RSD of the analytical result, RSDn,ax- Then the QL can be calculated using... 

The first group of sensor properties in Fig. 1.15 is concerned with the quality of results obtained in analytical processes involving a (bio)chemical sensor. All of them are obvious targets of analytical tasks [3]. As shown in the following section, the accuracy of the analytical results relies on a high reproducibility or repeatability, a steep slope of the calibration curve (or a low detection or quantification limit) and the absence of physical, chemical and physico-chemical interferences from the sample matrix. Sensors should ideally meet these essential requisites. Otherwise, they should be discarded for routine analytical use however great their academic interest may be. 

Immunochemical approaches are cheaper, readily adaptable, rapid, portable, and reduce the need for expensive analytical equipment. They can also be used to simultaneously assay a large number of samples over a short period of time. One of the major factors that still hmits the use of this technique in the detection of a wider range of PPCPs in the environment is the lack of suitable antibodies sensitive to most PPCPs that occur in the environment. Furthermore, immunoassay accuracy can be susceptible to cross reactions and other effects from the matrix, giving false positives in some instances (Huang and Sedlak, 2001). Thus, it is recommended that immunoassay analytical results be validated with GC- or LC-based methods. 

Comparing this value with the order a Zaym result in (3.101) we see that the difference between the exact numerical result and analytic calculation up to order a Zay is about 0.015 kHz for the IS -level in hydrogen, and, taking into account the accuracy of experimental results, one may use analytic results for comparison of the theory and experiment without loss of accuracy. A similar conclusion is valid for other hydrogen levels. 

A breakthrough was achieved a few years ago when it was realized that an anal dic calculation of the deuterium recoil, structure and polarizability corrections is possible in the zero range approximation [76, 77]. An analytic result for the difference in (12.29), obtained as a result of a nice calculation in [77], is numerically equal 44 kHz, and within the accuracy of the zero range approximation perfectly explains the difference between the experimental result and the sum of the nonrecoil corrections. More accurate calculations of the nuclear effects in the deuterium hyperfine structure beyond the zero range approximation are feasible, and the theory of recoil and nuclear corrections was later improved in a number of papers [78, 79, 80, 81, 82]. Comparison of the results of these works with the experimental data on the deuterium hyperfine splitting may be used as a test of the deuteron models and state of the art of the nuclear calculations. 

We have presented a statistical experimental design and a protocol to use in evaluating laboratory data to determine whether the sampling and analytical method tested meets a defined accuracy criterion. The accuracy is defined relative to a single measurement from the test method rather than for a mean of several replicate test results. Accuracy here is the difference between the test result and the "true value, and thus, must combine the two sources of measurement error ... 

The process of providing an answer to a particular analytical problem is presented in Figure 2. The analytical system—which is a defined method protocol, applicable to a specified type of test material and to a defined concentration rate of the analyte —must be fit for a particular analytical purpose [4]. This analytical purpose reflects the achievement of analytical results with an acceptable standard of accuracy. Without a statement of uncertainty, a result cannot be interpreted and, as such, has no value [8]. A result must be expressed with its expanded uncertainty, which in general represents a 95% confidence interval around the result. The probability that the mean measurement value is included in the expanded uncertainty is 95%, provided that it is an unbiased value which is made traceable to an internationally recognized reference or standard. In this way, the establishment of trace-ability and the calculation of MU are linked to each other. Before MU is estimated, it must be demonstrated that the result is traceable to a reference or standard which is assumed to represent the truth [9,10]. 

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