Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data117Using Table 4.18, we find that the critical value for G(0.05,9) is 2.215. BecauseG exp is greater than G(0.05,9), we can assume that the penny weighing2.514 g is an outlier.For Chauvenet’s criterion, the critical probability is (2×9) –1 , or 0.0556.The value of z is the same as G exp , or 2.64. Using Appendix 3, the probabilityfor z = 2.64 is 0.00415. Because the probability of obtaining a mass of0.2514 g is less than the critical probability, we can assume that the pennyweighing 2.514 g is an outlier.You should exercise caution when using a significance test for outliersbecause there is a chance you will reject a valid result. In addition, youshould avoid rejecting an outlier if it leads to a precision that is unreasonablybetter than that expected based on a propagation of uncertainty. Giventhese two concerns it is not surprising that some statisticians caution againstthe removal of outliers. 10On the other hand, testing for outliers can provide useful information ifyou try to understand the source of the suspected outlier. For example, theoutlier in Table 4.16 represents a significant change in the mass of a penny(an approximately 17% decrease in mass), which is the result of a changein the composition of the U.S. penny. In 1982 the composition of a U.S.penny was changed from a brass alloy consisting of 95% w/w Cu and 5%w/w Zn, to a zinc core covered with copper. 11 The pennies in Table 4.16,therefore, were drawn from different populations.4GDetection LimitsThe International Union of Pure and Applied Chemistry (IUPAC) definesa method’s detection limit as the smallest concentration or absoluteamount of analyte that has a signal significantly larger than the signal froma suitable blank. 12 Although our interest is in the amount of analyte, in thissection we will define the detection limit in terms of the analyte’s signal.Knowing the signal you can calculate the analyte’s concentration, C A , orthe moles of analyte, n A , using the equationsS A = k A C A or S A = k A n Awhere k is the method’s sensitivity.Let’s translate the IUPAC definition of the detection limit into a mathematicalform by letting S mb represent the average signal for a method blank,and letting s mb represent the method blank’s standard deviation. The nullhypothesis is that the analyte is not present in the sample, and the alterna-You also can adopt a more stringent requirementfor rejecting data. When usingthe Grubb’s test, for example, the ISO5752 guidelines suggest retaining a valueif the probability for rejecting it is greaterthan a = 0.05, and flagging a value as a“straggler” if the probability for rejectingit is between a = 0.05 and 0.01. A “straggler”is retained unless there is compellingreason for its rejection. The guidelines recommendusing a = 0.01 as the minimumcriterion for rejecting a data point.See Chapter 3 for a review of these equations.10 Deming, W. E. Statistical Analysis of Data; Wiley: New York, 1943 (republished by Dover: NewYork, 1961); p. 171.11 Richardson, T. H. J. Chem. Educ. 1991, 68, 310–311.12 IUPAC Compendium of Chemical Technology, Electronic Version, http://goldbook.iupac.org/D01629.html