Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data75Table 4.8 Replicate Determinations of the Mass of aSingle Circulating U. S. PennyReplicate Mass (g) Replicate Mass (g)1 3.025 6 3.0232 3.024 7 3.0223 3.028 8 3.0214 3.027 9 3.0265 3.028 10 3.024To evaluate the effect of indeterminate measurement error on our analysisof the mass of a circulating United States penny, we might make severaldeterminations for the mass of a single penny (Table 4.8). The standarddeviation for our original experiment (see Table 4.1) is 0.051 g, and it is0.0024 g for the data in Table 4.8. The significantly better precision whendetermining the mass of a single penny suggests that the precision of ouranalysis is not limited by the balance. A more likely source of indeterminateerror is a significant variability in the masses of individual pennies.4B.3 Error and UncertaintyAnalytical chemists make a distinction between error and uncertainty. 3 Erroris the difference between a single measurement or result and its expectedvalue. In other words, error is a measure of bias. As discussed earlier,we can divide error into determinate and indeterminate sources. Althoughwe can correct for determinate errors, the indeterminate portion of the errorremains. With statistical significance testing, which is discussed later inthis chapter, we can determine if our results show evidence of bias.Uncertainty expresses the range of possible values for a measurementor result. Note that this definition of uncertainty is not the same as ourdefinition of precision. We calculate precision from our experimental data,providing an estimate of indeterminate errors. Uncertainty accounts forall errors—both determinate and indeterminate—that might reasonablyaffect a measurement or result. Although we always try to correct determinateerrors before beginning an analysis, the correction itself is subject touncertainty.Here is an example to help illustrate the difference between precisionand uncertainty. Suppose you purchase a 10-mL Class A pipet from a laboratorysupply company and use it without any additional calibration. Thepipet’s tolerance of ±0.02 mL is its uncertainty because your best estimateof its expected volume is 10.00 mL ± 0.02 mL. This uncertainty is primarilydeterminate error. If you use the pipet to dispense several replicateportions of solution, the resulting standard deviation is the pipet’s precision.Table 4.9 shows results for ten such trials, with a mean of 9.992 mL and astandard deviation of ±0.006 mL. This standard deviation is the precision3 Ellison, S.; Wegscheider, W.; Williams, A. Anal. Chem. 1997, 69, 607A–613A.In Section 4E we will discuss a statisticalmethod—the F-test—that you can use toshow that this difference is significant.See Table 4.2 for the tolerance of a 10-mLclass A transfer pipet.