Analytical Chem istry - DePauw University

Chapter 7 Collecting and Preparing Samples287Percent of Overall Variance Due to the Method1008060402000 1 2 3 4 5s samp /s methFigure 7.2 The blue curve shows the method’s contributionto the overall variance, s 2 , as a function of the relativemagnitude of the standard deviation in sampling, s samp ,and the method’s standard deviation, s meth . The dashedred line shows that the method accounts for only 10% ofthe overall variance when s samp = 3 × s meth . Understandingthe relative importance of potential sources of indeterminateerror is important when considering how toimprove the overall precision of the analysis.Example 7.1A quantitative analysis gives a mean concentration of 12.6 ppm for ananalyte. The method’s standard deviation is 1.1 ppm and the standarddeviation for sampling is 2.1 ppm. (a) What is the overall variance for theanalysis? (b) By how much does the overall variance change if we improves meth by 10% to 0.99 ppm? (c) By how much does the overall variancechange if we improve s samp by 10% to 1.89 ppm?So l u t i o n(a) The overall variance is2 2 2 2 2s = s + s = ( 21 . ppm) + ( 11 . ppm) = 56 . ppm 2samp meth(b) Improving the method’s standard deviation changes the overall variancetos 2 = ( 21 . ppm) 2 + ( 099 . ppm) 2 = 5.4 ppm 2Improving the method’s standard deviation by 10% improves theoverall variance by approximately 4%.(c) Changing the standard deviation for samplings 2 2 2= (. 19ppm) + ( 11 . ppm) = 48 . ppm 2improves the overall variance by almost 15%. As expected, becauses samp is larger than s meth , we obtain a bigger improvement in the overallvariance when we focus our attention on sampling problems.Practice Exercise 7.1Suppose you wish to reduce theoverall variance in Example 7.1to 5.0 ppm 2 . If you focus on themethod, by what percentage doyou need to reduce s meth ? If youfocus on the sampling, by whatpercentage do you need to reduces samp ?Click here to review your answerto this exerciseTo determine which step has the greatest effect on the overall variance,we need to measure both s samp and s meth . The analysis of replicate samples