Systematic errors laboratory analysis

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. ... 

The first sample to be analyzed is the field blank. If its spike recovery is unacceptable, indicating that a systematic error is present, then a laboratory method blank. Dp, is prepared and analyzed. If the spike recovery for the method blank is also unsatisfactory, then the systematic error originated in the laboratory. An acceptable spike recovery for the method blank, however, indicates that the systematic error occurred in the field or during transport to the laboratory. Systematic errors in the laboratory can be corrected, and the analysis continued. Any systematic errors occurring in the field, however, cast uncertainty on the quality of the samples, making it necessary to collect new samples. 

The apphed pretreatment techniques were digestion with a combination of acids in the pressurized or atmospheric mode, programmed dry ashing, microwave digestion and irradiation with thermal neutrons. The analytical methods of final determination, at least four different for each element, covered all modern plasma techniques, various AAS modes, voltammetry, instrumental and radiochemical neutron activation analysis and isotope dilution MS. Each participating laboratory was requested to make a minimum of five independent rephcate determinations of each element on at least two different bottles on different days. Moreover, a series of different steps was undertaken in order to ensure that no substantial systematic errors were left undetected. 

A final point is the value of earlier (old) validation data for actual measurements. In a study about the source of error in trace analysis, Horwitz et al. showed that systematic errors are rare and the majority of errors are random. In other words, the performance of a laboratory will vary with time, because time is related to other instruments, staff, chemicals, etc., and these are the main sources of performance variation. Subsequently, actual performance verification data must be generated to establish method performance for all analytes and matrices for which results will be reported. 

We will begin by taking a look at the detailed aspects of a basic problem that confronts most analytical laboratories. This is the problem of comparing two quantitative methods performed by different operators or at different locations. This is an area that is not restricted to spectroscopic analysis many of the concepts we describe here can be applied to evaluating the results from any form of chemical analysis. In our case we will examine a comparison of two standard methods to determine precision, accuracy, and systematic errors (bias) for each of the methods and laboratories involved in an analytical test. As it happens, in the case we use for our example, one of the analytical methods is spectroscopic and the other is an HPLC method. 

Table 35-3 illustrates the ANOVA results comparing laboratories (i.e., different locations) performing the same METHOD A for analysis. This statistical test indicates that for the mid-level concentration spiked samples (i.e. 4 and 4 at 3.40 and 3.61% levels, respectively) difference in reported average values occurred. However, this trend did not continue for the highest concentration sample (i.e., Sample No. 6) with a concentration of 3.80%. The Lab 1 was slightly lower in reported value for Samples 4 and 5. There is no significant systematic error observed between laboratories using the METHOD A. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

Systematic Error in Laboratory Analysis. Dr. Currie "l would like to raise a nasty issue that is pertinent to some of the comments I am hearing with respect to complex measurements and environmental systems and that is, it is rare for me to see much... 

Collaborative Testing. A second approach to assessing accuracy, when no certified reference material is available, may be used in conjunction with analysis by independent methods and in-house materials. Sample exhanges with other laboratories can help establish the existence or absence of systematic errors in a method. Collaborative tests are most useful in this regard when some of the participating laboratories use different sample preparation and quantification. The utility of independent analysis methods and comparisons between destructive and non-destructive analysis is again emphasized here. 

Table III shows the results on the various elements reported. The elements are arranged alphabetically by symbol. Cases where we have extrapolated or averaged data are so marked (—e.g., the averages of results for laboratory 33 in copper). Table III is the most important table here and contains all the information necessary to compile Tables IV, V, and VI. The latter are included to facilitate data comparison and interpretations. Table III is the true result of this phase of the study although we interpret it in some detail below, this is not absolutely necessary. A superficial perusal of Table III reveals discrepancies which must be caused by systematic errors in the various laboratories. A repeat of the comparative analysis program, with more uniform samples, coupled with circulation of known standards, should reduce this variation.

This is the common form of the F-ratio because reproducibility is usually (much) greater than repeatability. Following the conventions of analysis of variance, which assume that repeatability is influenced by random errors whereas systematic errors might influence reproducibility and therefore yield larger values of s%prod, we have to use one-sided critical values F (feprodi frepeat-, < = 1 - ) In this case we are allowed to assume that variation of the reproducibility (over all laboratories) is random in nature. 

A control chart can be used to determine whether a method is under control over time it is not, however, able to detect a systematic error which is present from the moment of introduction of the method in a laboratory. Results should hence be verified by other methods. As stressed later in this chapter, all methods have their own particular sources of error which are related to one or several analytical steps (Quevauviller et al., 1996a). An independent method should be used to verify the results of routine analysis. If the results of both methods are in good agreement, it can be concluded that the results of the routine analysis are unlikely to be affected by a contribution of a systematic nature (e.g. insufficient extraction). This conclusion is stronger when the two methods differ widely. If the methods have similarities, such as an extraction step, a comparison of the results would probably lead to conclusions concerning the accuracy of the method of final determination, and not as regards the analytical result as a whole. 

Statistics should follow the technical scrutiny, not the other way round. A statistical analysis of data of an interlaboratory study cannot explain deviating results nor can alone give information on the accuracy of the results. Statistics only treat a population of data and provide information on the statistical characteristics of this population. The results of the statistical treatment may give rise to discussions on particular data not belonging to the rest of the population, but outlying data can sometimes be closer to the true value than the bulk of the population (Griepink et al., 1993). If no systematic errors affect the population of data, various statistical tests may be applied to the results, which can be treated either as individual data or as means of laboratory means. When different methods are applied, the statistical treatment is usually based on the mean values of replicate determinations. Examples of statistical tests used for certification purposes are described elsewhere (Horwitz, 1991). Together with the technical evaluation of the results, the statistical evaluation forms the basis for the conclusions to be drawn and the possible actions to be taken. 

On-site water-quality measurements are carried out predominantly to monitor effective purging of water at the sampling point before sample collection and to measure unstable parameters that cannot be subsequently reliably determined in the laboratory. On-site measurements can also be used to provide a check on a subsequent laboratory analysis. For example, provided that the on-site SEC is measured accurately, it can be compared with the SEC estimated from the laboratory chemical analysis by one of a number of geochemical programmes. This check can be useful for spotting major errors, such as dilution or typographical errors, as well as systematic errors in analytical methodology. 

According to Malyj and Griffiths (1983), determining the equilibrium rotational or vibrational temperature by the Stokes/anti-Stokes ratio is not as simple and straightforward as the equations imply. The authors discuss the problems which evolve as a result of using standard lamps and show how to meet these difficulties by using reference materials to measure the temperature as well as to determine the instrumental spectral response function. The list of suitable materials includes vitreous silica and liquid cyclohexane, which are easy to handle and available in most laboratories. The publication includes a detailed statistical analysis of systematic errors and also describes tests with a number of transparent materials. 

Normally, CRMs are used for the verification of accuracy, precision, and reliability of the results of analysis carried out in a laboratory (i.e., for checking the quality of its routine work). The CRM is analyzed at specific intervals and the results obtained are used to draw control charts (e.g., Shewhart chart) [63]. This allows visual assessment of the measurement system, the emergence of systematic errors, etc. Application of CRMs for the constmction of control charts is advantagous because of the homogeneity and stability of CRMs, and the ability to assess the accuracy of the results obtained in the laboratory by comparison with the certified value. 

Analysis of systematic errors in the determination of hydrocarbons in water can be achieved by use of Youden plots after transformation of the results to an overall mean of Mtotal=0 and a standard deviation of Stotal=l (Fig. 3). Almost all laboratories are distributed around the 45° line indicating that most of the variation was systematic rather than random, particularly at higher mineral oil concentrations (sample pair S2/S4, Fig. 3B). Results located within the interval Mtotal 2 Stotal indicate sufficient proficiency of the participating laboratories in performing the determination of hydrocarbons in water... 

To test the quality of the work of a commercial laboratory, duplicate analyses of a purified benzoic acid (68.8% C, 4.953% H) sample were requested. It is assumed that the relative standard deviation of the method is cr = 4 ppt for carbon and 6 ppt for hydrogen. The means of the reported results are 68.5% C and 4.882% H. At the 95% confidence level, is there any indication of systematic error in either analysis ... 

Atomic absorption, optical emission and atomic fluorescence as well as plasma mass spectrometry and new approaches such as laser enhanced ionization now represent strong tools for elemental analysis including speciation and are found in many analytical laboratories. Their power of detection, reliability in terms of systematic errors and their costs reflecting the economic aspects should be compared with those of other methods of analysis, when it comes to the development of strategies for solving analytical problems (Table 20). 

Relaxation Rate Measurements. - Measurement and analysis of traditional laboratory frame heteronuclear relaxation parameters R, R2 and NOE were summarised by Palmer in a review. The publication concentrates on the dynamic processes on ps-ns time scale in proteins. The theoretical part has a general character, while the experimental section and examples deal mainly with N relaxation. A source of systematic error in the commonly used T2 CPMG measurements was highlighted by Korzhnev et al The authors observed offset-dependent difference between T2 and Tip values. This difference was attributed to the off-resonance effects of N 180° pulses. When uncorrected, the error can be misinterpreted as a contribution from a slow conformational exchange. The authors suggested a numerical correction procedure. 

When the paired departments use fundamentally different methods of analysis, as is possible with serum enzyme determinations, for instance, the comparisons may be of only limited value. However, many laboratories now use AutoAnalyzer techniques for 60-80% of their total work, and a start on regular interlaboratory comparisons of these methods should be worthwhile and involve relatively little additional effort. Although the AutoAnalyzer methods used in the different laboratories might themselves show some differences in detail, the information provided by these comparisons should serve to detect in one laboratory the development of some systematic error in the routine performance of a method at an earlier stage than if the laboratory had itself been solely responsible for its assessment of results of quality control programs. 

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