Errors in quantitative analysis

Since quantitative studies play a dominant role in any analytical laboratory, it must be accepted that the errors that occur in such studies are of supreme importance. Our guiding principle will be that no quantitative results are of any value unless they are accompanied by some estimate of the errors inherent in them. This principle naturally applies not only to analytical chemistry but to any field of study in which numerical experimental results are obtained. It is illustrated by the following simple examples, which also foreshadow the types of statistical problem we shall meet and solve in subsequent chapters. 

Suppose a chemist synthesizes an analytical reagent that is believed to be entirely new. The compound is studied using a spectrometric method and gives a value of 104 (normally, most of our results will be cited in carefully chosen units, but in this hypothetical example purely arbitrary units can be used). From suitable reference books, the chemist finds that no compoimd previously discovered has yielded a value of more than 100 when studied by the same method under the same experimental conditions. The question thus naturally arises, has our chemist really discovered a new compound The answer to this question evidently lies in the degree of reliance that we can place on that experimental value of 104. What errors are associated with it If further study indicates that the result is correct to within 2 (arbitrary) units, i.e. the true value probably lies in the range 104 2, then a new material has probably been discovered. If, however, investigations show that the error may amount to 10 units (i.e. 104 10), then it is quite likely that the true value is actually less than 100, in which case a new discovery is far from certain. So a knowledge of the experimental errors is crucial (in this case as in every other) to the proper interpretation of the results. In statistical terms this example would involve the comparison of the experimental result (104) with a reference value (100) this topic is studied in detail in Chapter 3. 

Analysts commonly perform several replicate determinations in the course of a single experiment. (The value and significance of such replicates are discussed in detail in the next chapter.) Suppose an analyst performs a titrimetric experiment four times and obtains values of 24.69, 24.73, 24.77 and 25.39 ml. (Note that titration values are reported to the nearest 0.01 ml this point is also discussed further in Chapter 2.) All four values are different, because of the variations inherent in the measurements, and the fourth value (25.39 ml) is substantially different from the other three. So can this fourth value be safely rejected, so that (for example) the mean titre is reported as 24.73 ml, the average of the other three readings In statistical terms, is the value 25.39 ml an outlier The important topic of outlier rejection is discussed in detail in Chapters 3 and 6. 

Another frequent problem involves the comparison of two (or more) sets of results. Suppose that an analyst measures the vanadium content of a steel sample by two separate methods. With the first method the average value obtained is 1.04%, with an estimated error of 0.07%, and with the second method, the average value is 

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Royston, G. C., Comments on Unrecognized Systematic Errors in Quantitative Analysis in Gas Chromatography, Ana/. Chem. 50, 1978, 1005. 

The accuracy and precision of carotenoid quantification by HPLC depend on the standard purity and measurement of the peak areas thus quantification of overlapping peaks can cause high variation of peak areas. In addition, preparation and dilution of standard and sample solutions are among the main causes of error in quantitative analysis. For example, the absorbance levels at of lutein in concentrations up to 10 mM have a linear relationship between concentration and absorbance in hexane and MeOH on the other hand, the absorbance of P-carotene in hexane increased linearly with increasing concentration, whereas in MeOH, its absorbance increased linearly up to 5 mM but non-linearly at increasingly higher concentrations. In other words, when a stock solution of carotenoids is prepared, care should be taken to ensure that the compounds are fuUy soluble at the desired concentrations in a particular solvent. 

As a result of the mediocre (energy) resolution of the Si(Li) detector, the probability of overlap between several lines is significant, which may entail a certain ambiguity in the interpretation of spectra and serious errors in quantitative analysis (for example, the Mo La and S Ka lines are superimposed). 

Henrion, A., Reduction of systematic errors in quantitative analysis by isotope-dilution mass spectrometry (IDMS) an iterative method, Fresenius Z. Anal. Chem., 350, 657-658 (1994). 

Interferences are physical or chemical processes that cause the signal from the analyte in the sample to be higher or lower than the signal from an equivalent standard. Interferences can therefore cause positive or negative errors in quantitative analysis. There are two major classes of interferences in AAS, spectral interferences and nonspectral... 

The discrimination factor has also been used in error analysis in quantitative HPLC (22). Since resolution is not sensitive to relative p height and the error in quantitation depends strongly on the location of the valley between the peaks, do is a valid parameter for duuacterizing errors in quantitative analysis. The error can be expressed using the fractional area F, and fractional height for the smallest pe i (the one for which the error is the higliest) ... 

Interferences are physical or chemical processes that cause the signal from the analyte in the sample to be higher or lower than the signal from an equivalent standard. Interferences can therefore cause positive or negative errors in quantitative analysis. There are two major classes of interferences in AAS, spectral interferences and nonspectral interferences. Nonspectral interferences are those that affect the formation of analyte free atoms. Nonspectral interferences include chemical interference, ionization interference, and solvent effects (or matrix interference). Spectral interferences cause the amount of light absorbed to be erroneously high due to absorption by a species other than the analyte atom. While all techniques suffer from interferences to some extent, AAS is much less prone to spectral interferences and nonspectral interferences than atomic anission spectrometry and X-ray fluorescence (XRF), the other major optical atomic spectroscopic techniques. 

The split mode has the advantage that the injected zone is narrow and the small sample aliquot entering the capillary avoids overloading the column. Although very flexible in practice, this mode has a number of disadvantages. In many cases mass discrimination among analytes is observed, especially when their volatilities are very different, and this can lead to systematic errors in quantitative analysis. Another disadvantage, especially in trace analysis, arises from the (sometimes small) fraction of the analytes that is transferred into the capillary i.e. the majority exits via the split outlet. 

These examples represent only a fraction of the possible problems arising from the occurrence of experimental errors in quantitative analysis. But such problems have to be tackled if the quantitative data are to have any real meaning. Clearly, therefore, we must study the various types of error in more detail. 

Four techniques are commonly used in quantitative analysis the normalization method, the external standard method, the internal standard method, and the standard addition method. Whatever method is used, the accuracy often depends on the sample preparation and on the injection technique. Nowadays these are two main sources of error in quantitative analysis. The quantitative results produced by PCGC and CGC are comparable. 

First, it is always better to optimize the collision energy that can balance the fragment intensities of all the ions of the entire class of interest for quantification of lipid species by tandem MS in shotgun lipidomics even more than one internal standards are employed in the method. Similarly, optimization of the SRM/MRM conditions for individual species in an LC-MS/MS method is not recommended when interest is to quantify all the species of a class, unless a calibration curve for each individual species is established under the identical conditions, since optimization of MRM conditions for individual lipid species leads to an incomparable response factor of the species of interest to that of the selected internal standard. In both cases of shotgun lipidomics and LC-MS/MS analyses, different collision energies applied for different species could lead to substantial errors in quantitative analysis, as discussed previously [22]. Careful attention to CID energy must be exercised if accurate quantification is a goal. 

In several of the previous sections of this chapter some of the sources of error in quantitative analysis were mentioned briefly. A discussion of these and other possible errors, to give a better understanding of their causes and effects on results, follows. 

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