Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data133precision. A propagation of uncertainty allows us to estimate how thesedeterminate and indeterminate errors will affect our results.When we analyze a sample several times the distribution of the resultsis described by a probability distribution, two examples of which are thebinomial distribution and the normal distribution. Knowing the type ofdistribution allows us to determine the probability of obtaining a particularrange of results. For a normal distribution we express this range as a confidenceinterval.A statistical analysis allows us to determine whether our results are significantlydifferent from known values, or from values obtained by otheranalysts, by other methods of analysis, or for other samples. We can use at-test to compare mean values and an F-test to compare precisions. To comparetwo sets of data you must first determine whether the data is paired orunpaired. For unpaired data you must also decide if the standard deviationscan be pooled. A decision about whether to retain an outlying value canbe made using Dixon’s Q-test, Grubb’s test, or Chauvenet’s criterion. Youshould be sure to exercise caution when deciding to reject an outlier.Finally, the detection limit is a statistical statement about the smallestamount of analyte that we can detect with confidence. A detection limit isnot exact since its value depends on how willing we are to falsely report theanalyte’s presence or absence in a sample. When reporting a detection limityou should clearly indicate how you arrived at its value.4KProblems1. The following masses were recorded for 12 different U.S. quarters (allgiven in grams):5.683 5.549 5.548 5.5525.620 5.536 5.539 5.6845.551 5.552 5.554 5.632Report the mean, median, range, standard deviation and variance forthis data.2. A determination of acetaminophen in 10 separate tablets of ExcedrinExtra Strength Pain Reliever gives the following results (in mg). 16224.3 240.4 246.3 239.4 253.1261.7 229.4 255.5 235.5 249.7Answers, but not worked solutions, tomost end-of-chapter problems are availablehere.Many of the problems that follow require accessto statistical tables. For your convenience,here are hyperlinks to the appendices containingthese tables.Appendix 3: Single-Sided Normal DistributionAppendix 4: Critical Values for the t-TestAppendix 5: Critical Values for the F-TestAppendix 6: Critical Values for Dixon’s Q-TestAppendix 7: Critical Values for Grubb’s Test(a) Report the mean, median, range, standard deviation and variancefor this data. (b) Assuming that X and s 2 are good approximations form and s 2 , and that the population is normally distributed, what per-16 Simonian, M. H.; Dinh, S.; Fray, L. A. Spectroscopy 1993, 8(6), 37–47.