Analytical Chem istry - DePauw University

288 Analytical Chemistry 2.0There are several ways to minimize thestandard deviation for sampling. Here aretwo examples. One approach is to use astandard reference material (SRM) thathas been carefully prepared to minimizeindeterminate sampling errors. When thesample is homogeneous—as is the case,for example, with aqueous samples—auseful approach is to conduct replicateanalyses on a single sample.provides an estimate of the overall variance. To determine the method’svariance we analyze samples under conditions where we may assume thatthe sampling variance is negligible. The sampling variance is determinedby difference.Example 7.2The following data were collected as part of a study to determine the effectof sampling variance on the analysis of drug-animal feed formulations. 2% Drug (w/w) % Drug (w/w)0.0114 0.0099 0.0105 0.0105 0.0109 0.01070.0102 0.0106 0.0087 0.0103 0.0103 0.01040.0100 0.0095 0.0098 0.0101 0.0101 0.01030.0105 0.0095 0.0097The data on the left were obtained under conditions where both s samp ands meth contribute to the overall variance. The data on the right were obtainedunder conditions where s samp is known to be insignificant. Determine theoverall variance, and the standard deviations due to sampling and the analyticalmethod. To which factor—sampling or the method—should youturn your attention if you want to improve the precision of the analysis?See Chapter 4 for a review of how to calculatethe variance.So l u t i o nUsing the data on the left, the overall variance, s 2 , is 4.71 × 10 –7 . To find2the method’s contribution to the overall variance, s meth, we use the data onthe right, obtaining a value of 7.00 × 10 –8 . The variance due to sampling,, is2s samp2 2 2 −7 −8s = s − s = 471 . × 10 − 7. 00× 10 = 401 . × 10 −7sampmethConverting variances to standard deviations gives s samp as 6.32 × 10 –4 ands meth as 2.65 × 10 –4 . Because s samp is more than twice as large as s meth , improvingthe precision of the sampling process has the greatest impact onthe overall precision.2 Fricke, G. H.; Mischler, P. G.; Staffieri, F. P.; Houmyer, C. L. Anal. Chem. 1987, 59, 1213–1217.Practice Exercise 7.2A polymer’s density provides a measure of its crystallinity. The standarddeviation for the determination of density using a single sample of a polymeris 1.96 × 10 –3 g/cm 3 . The standard deviation when using differentsamples of the polymer is 3.65 × 10 –2 g/cm 3 . Determine the standarddeviations due to sampling and the analytical method.Click here to review your answer to this exercise.