Evaluating Analytical Data

When designing and evaluating an analytical method, we usually make three separate considerations of experimental error. First, before beginning an analysis, errors associated with each measurement are evaluated to ensure that their cumulative effect will not limit the utility of the analysis. Errors known or believed to affect the result can then be minimized. Second, during the analysis the measurement process is monitored, ensuring that it remains under control. Finally, at the end of the analysis the quality of the measurements and the result are evaluated and compared with the original design criteria. This chapter is an introduction to the sources and evaluation of errors in analytical measurements, the effect of measurement error on the result of an analysis, and the statistical analysis of data. 

One way to characterize the data in Table 4.1 is to assume that the masses of individual pennies are scattered around a central value that provides the best estimate of a penny s true mass. Two common ways to report this estimate of central tendency are the mean and the median. 

Mean The mean, X, is the numerical average obtained by dividing the sum of the individual measurements by the number of measurements 

Masses of Seven United States Pennies in Circulation 

The mean is the most common estimator of central tendency. It is not considered a robust estimator, however, because extreme measurements, those much larger or smaller than the remainder of the data, strongly influence the mean s value. For example, mistakenly recording the mass of the fourth penny as 31.07 g instead of 3.107 g, changes the mean from 3.117 g to 7.112 g  

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Linear least-squares analysis is quite easy with Excel. This type of analysis can be accomplished in several ways by using the equations presented in this chapter, by employing the basic built-in functions of Excel, or by using the regression data analysis tool. Because the built-in functions are the easiest of these options, we explore them in detail here and see how they may be used to evaluate analytical data. 

Such a coupled expert system would be able not only to evaluate analytical data, but to adjust them to improve both their internal consistency and the accuracy with which they represent the chemistry of water in the formation. This evaluation and adjustment, if done at all, now requires manual calculation and geochemical modeling by a human expert. Manual calculations are likely to be slower and their results less consistent from expert to expert, or from time to time from a single expert, than results guided by an expert system program. 

In analytical chemistry, statistics are needed to evaluate analytical data and measurements and to preprocess, reduce, and interpret the data. 

For more Information on the application of spreadsheets in evaluating analytical data, sec S. R. Crouch and F. J. Holler. Applications of Microsoft Excel in Analytical Chemistry, Belmont. CA Brooks/Cole, 2004. 

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