Handling systematic errors

Much of the remainder of this book will deal with the evaluation of random errors, which can be studied by a wide range of statistical methods. In many cases we shall assume for convenience that systematic errors are absent (though methods which test for the occurrence of systematic errors will be described). But first we must discuss systematic errors in more detail - how they arise, and how they may be countered. The titration example above shows that systematic errors cause the mean value of a set of replicate measurements to deviate from the true value. It follows that (a) in contrast to random errors, systematic errors cannot be revealed merely by making repeated measurements, and that (b) unless the true result of the analysis is known in advance - an unlikely situation - very large systematic errors might occur, but go entirely undetected unless suitable precautions are taken. In other words, it is all too easy to overlook substantial sources of systematic error. A few examples will clarify both the possible problems and their solutions. 

The levels of transition metals in biological samples such as blood serum are frequently important. Many determinations have been made of the levels of (for example) chromium in serum - with startling results. Different workers, all studying pooled serum samples from healthy subjects, have obtained chromium 

Systematic errors arise not only from procedures or apparatus they can also arise from human bias. Some chemists suffer from astigmatism or colour-blindness (the latter is more common amongst men than women) which might introduce errors into their readings of instruments and other observations. Many authors have reported various types of number bias, for example a tendency to favour even over odd numbers, or 0 and 5 over other digits, in the reporting of results. It is thus apparent that systematic errors of several kinds are a constant, and often hidden, risk for the analyst, so the most careful steps to minimize them must be considered. 

The second line of defence against systematic errors lies in the design of the experiment at every stage. We have already seen (Section 1.4) that weighing by 

A further check on the occurrence of systematic errors in a method is to compare the results with those obtained from a different method, if two unrelated methods are used to perform one analysis, and if they consistently yield results showing only random differences, it is a reasonable presumption that no significant systematic errors are present. For this approach to be valid, each step of the two experiments has to be independent. Thus in the case of serum chromium determinations, it would not be sufficient to replace the atomic-absorption spectrometry step by a colorimetric method or by plasma spectrometry. The systematic errors would only be revealed by altering the sampling methods also, e.g. by minimizing or eliminating the use of stainless-steel equipment. A further important point is that comparisons must be made over the whole of the concentration range for which an analytical procedure is 

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The presence of systematic errors is, potentially, the most important source of uncertainty. There is no possibility to handle systematic errors using statistics statistical methods may indicate their presence, no more. Systematic errors in the chemical model have been mentioned. In addition there may be systematic errors in the methods used. By comparing experimental data obtained with different experimental methods one can obtain an indication of the presence and magnitude of such errors. The systematic errors of this type are accounted for both in the review of the literature and when taking the... 

Sample handling high flexibility regarding sample concentration, solvent, and column temperature optimal reproducibility of absolute retention times demand for analyses requiring high accuracy high risk of systematic errors. 

The G-BASE project collects samples in random number order (Plant, 1973), as this helps identify any correctable systematic errors introduced during sample preparation and analysis, processes in which the samples are handled in numeric order. For every block of one hundred numbers, five numbers are reserved for control samples so when they are submitted within a batch of samples they are blind to the analyst. The control samples inserted are one duplicate sample, two replicate samples, two blanks, and two secondary reference materials (SRM) used to monitor accuracy and precision as well as to level data between different field campaigns (see Johnson et al, 2008). Along with the original sample ofthe duplicate pair, this means 8% of samples submitted are control samples, a point not to be overlooked in setting the budget for analyses. 

The errors inherent in any physical measurement are of two kinds. The first category, which is relatively simple to deal with, involves errors that are random. The second category, which is more difficult to detect and so also difficult to handle, includes systematic errors, i.e., errors which are not random but inherent in the reaction studied or the methods employed. A typical example of the latter would be the small contribution of a secondary reaction, the extent of which is determined by the concentrations and temperatures. It is thus inherent in the nature of the system observed, and the magnitude of the errors involved in neglecting this secondary reaction is not random but directly related to the state of the system. Errors due to small amounts of secondary reactions are the most frequent type of systematic error encountered in kinetic studies. ... 

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. 

In Chapter 3 it was discussed how the presence of a random error can be handled by statistical tools. The precautions which must be taken by the experimenter not to violate the assumption of independencies of the experimental error is randomization, which allows certain time-dependent systematic errors to be broken down and turned into random errors. There are, however, sources of error which can be suspected to produce systematic deviations which cannot be counteracted by randomization. In such cases, forseeable sources of systematic variation can be brought under control by dividing the whole set of experiments into smaller blocks which can be run under more homogeneous conditions. By a proper arrangement of these blocks, the systematic variation can be isolated through comparison of the between-block variation. Some examples where splitting the series of experiments into blocks is appropriate are ... 

Nonspecific analytical methods, such as colorimetry and titrimetry, for determination of summary parameters were the earliest attempts to analyze surfactants in the environment. The main disadvantage of these methods is that, apart from surfactants, other interfering organic compounds from the environmental matrices are recorded too, resulting in systematic errors. Nevertheless, colorimetric and titrimetric methods are stiU widely used for determination of anionic, nonionic, and cationic surfactants because of their easy handling and the need for relatively simple apparatus. 

The validity of these titrations has been explored in a mass-spectrometric study by Oyne, Cruse, and Watson. It was concluded that systematic errors in using CINO titrations to determine [O] or (Br) under defined conditions would not exceed 15 %. The major technique iM oblems are the in ocurement of an adequately pure sample of ONO and the handling of this material, which is extremely corrosive towards stainless steel or monel valves. 

Table 5.12 lists the major sources of random and systematic errors encountered in x-ray spectrometry. Methods for handling these error sources are discussed in subsequent chapters. As Table 5.12 shows, the major sources of random error arise from counting errors and equipment instability. Equipment random error has improved to the point where this source of error is generally of very low order (i.e., approximately 0.05 to 0.1%). Thus, to increase analytical precision, the major systematic errors must be recognized and eliminated or reduced. 

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