Error, analytical systematic

It cannot be overemphasized that MU is different from error. The error of an individual analytical result, the difference between the result and the true value of the measurand, is always a single value [38]. Part of the value of a known error, the systematic error, can be used to correct a result. This means that after correction the result of an analysis may be very close to the true value. However, the uncertainty of the measurement may still be very large because there is doubt or limited knowledge about how close the result is to the value. Uncertainty is expressed as a range and applies to an analytical procedure and a specific sample type but to different determinations and thus measurement results. The value of the uncertainty cannot be used to correct a measurement result. 

In general, results from investigations based on measurements may be falsified by three principal types of errors gross, systematic, and random errors. In most cases gross errors are easily detected and avoidable. Systematic errors (so-called determinate errors) affect the accuracy and therefore the proximity of an empirical (experimental) result to the true result, which difference is called bias. Random errors (so-called indeterminate errors) influence the precision of analytical results. Sometimes precision is used synonymously with reproducibility and repeatability. Note that these are different measures of precision, which, in turn, is not related to the true value. 

Analytical results are subject to two types of errors, namely, systematic and random. Both will influence the accuracy of a test result. Accuracy has been... 

A second type of error, called systematic (or determinate) error, causes the mean of a data set to differ from the accepted value. For example, the mean of the results in Figure 5-1 has a systematic error of about —0.2 ppm Fe. The results of analysts 1 and 2 in Figure 5-3 have little systematic error, but the data of analysts 3 and 4 show systematic errors of about —0.7% and —1.2% nitrogen. In general, a systematic error in a series of replicate measurements causes all the results to be too high or too low. An example of a systematic error is the unsuspected loss of a volatile analyte while heating a sample. 

Systematic errors cause a bias from the true values which are hardly expressible in statistical terms. Most statistical handbooks neglect this analytical item, although it is a question of utmost importance for the analyst. The first question is always whether the error is systematic or random. This question cannot be answered in one determination, thus It will be dealt with later. 

Error sources in HPLC are so manifold that they cannot all be discussed completely. Nevertheless. one can distinguish between random errors and systematic errors. Whereas random errors are relatively easy to recognize and avoid, systematic errors often lead to false quantitative interpretation of chromatograms. Two simple ways of recognizing a systematic error in a newly developed (or newly applied) analytical method are either to test this new method with certified materials or—if an old (i.e., validated) method already exists—to compare the result from the old and the new methods. If the new method shows good reproducibility, a correction factor can be calculated easily by... 

Errors in the determination of the concentration of analyte species in the standard reference material that exceed the random errors associated with measurement precision are identified as systematic errors.These systematic errors can originate from a variety of sources. The most common source is an isobaric interference (see Chapter 8 on interferences). Other commonly observed systematic errors can result from matrix interferences. 

Gardone, M. J. Detection and Determination of Error in Analytical Methodology. Part 11. Gorrection for Gorrigible Systematic Error in the Gourse of Real Sample Analysis, /. Assoc. Off. Anal. Chem. 1983, 66, 1283-1294. 

A validation method used to evaluate the sources of random and systematic errors affecting an analytical method. 

The design of a collaborative test must provide the additional information needed to separate the effect of random error from that due to systematic errors introduced by the analysts. One simple approach, which is accepted by the Association of Official Analytical Chemists, is to have each analyst analyze two samples, X and Y, that are similar in both matrix and concentration of analyte. The results obtained by each analyst are plotted as a single point on a two-sample chart, using the result for one sample as the x-coordinate and the value for the other sample as the -coordinate. ... 

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. 

The "feedback loop in the analytical approach is maintained by a quality assurance program (Figure 15.1), whose objective is to control systematic and random sources of error.The underlying assumption of a quality assurance program is that results obtained when an analytical system is in statistical control are free of bias and are characterized by well-defined confidence intervals. When used properly, a quality assurance program identifies the practices necessary to bring a system into statistical control, allows us to determine if the system remains in statistical control, and suggests a course of corrective action when the system has fallen out of statistical control. 

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. 

Spike recoveries for samples are used to detect systematic errors due to the sample matrix or the stability of the sample after its collection. Ideally, samples should be spiked in the field at a concentration between 1 and 10 times the expected concentration of the analyte or 5 to 50 times the method s detection limit, whichever is larger. If the recovery for a field spike is unacceptable, then a sample is spiked in the laboratory and analyzed immediately. If the recovery for the laboratory spike is acceptable, then the poor recovery for the field spike may be due to the sample s deterioration during storage. When the recovery for the laboratory spike also is unacceptable, the most probable cause is a matrix-dependent relationship between the analytical signal and the concentration of the analyte. In this case the samples should be analyzed by the method of standard additions. Typical limits for acceptable spike recoveries for the analysis of waters and wastewaters are shown in Table 15.1. ... 

In the previous section we described several internal methods of quality assessment that provide quantitative estimates of the systematic and random errors present in an analytical system. Now we turn our attention to how this numerical information is incorporated into the written directives of a complete quality assurance program. Two approaches to developing quality assurance programs have been described a prescriptive approach, in which an exact method of quality assessment is prescribed and a performance-based approach, in which any form of quality assessment is acceptable, provided that an acceptable level of statistical control can be demonstrated. 

To sum up, in some instances the proposed tangent method and procedure of systematic error correction allows excluding the necessity of mathematical or chemical resolution of overlapped peak-shaped analytical signals. 

One possibility is that the curvature is an artifact introduced by a systematic error in the measurements. This is not unlikely, because rate constants may vary by orders of magnitude over a wide temperature range, necessitating different analytical methods or data treatments in different temperature regions. Careful experimental work should be able to identify such problems. 

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 accuracy of a determination may be defined as the concordance between it and the true or most probable value. It follows, therefore, that systematic errors cause a constant error (either too high or too low) and thus affect the accuracy of a result. For analytical methods there are two possible ways of determining the accuracy the so-called absolute method and the comparative method. 

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