Analytical Chem istry - DePauw University

68 Analytical Chemistry 2.0The convention for representing statisticalparameters is to use a Roman letter for avalue calculated from experimental data,and a Greek letter for the correspondingexpected value. For example, the experimentallydetermined mean is X , and itsunderlying expected value is μ. Likewise,the standard deviation by experiment is s,and the underlying expected value is s.It is possible, although unlikely, that thepositive and negative determinate errorswill offset each other, producing a resultwith no net error in accuracy.Practice Exercise 4.1The following data were collected as part of a quality control study forthe analysis of sodium in serum; results are concentrations of Na + inmmol/L.4B140 143 141 137 132 157 143 149 118 145Report the mean, the median, the range, the standard deviation, and thevariance for this data. This data is a portion of a larger data set from Andrew,D. F.; Herzberg, A. M. Data: A Collection of Problems for the Studentand Research Worker, Springer-Verlag:New York, 1985, pp. 151–155.Click here to review your answer to this exercise.Characterizing Experimental ErrorsCharacterizing the mass of a penny using the data in Table 4.1 suggeststwo questions. First, does our measure of central tendency agree with thepenny’s expected mass? Second, why is there so much variability in theindividual results? The first of these questions addresses the accuracy of ourmeasurements, and the second asks about their precision. In this section weconsider the types of experimental errors affecting accuracy and precision.4B.1 Errors Affecting AccuracyAccuracy is a measure of how close a measure of central tendency is to theexpected value, μ. We can express accuracy as either an absolute error, eor as a percent relative error, %e r .e= X −µ 4.2X%e = − µ × 100r4.3µAlthough equations 4.2 and 4.3 use the mean as the measure of centraltendency, we also can use the median.We call errors affecting the accuracy of an analysis determinate. Althoughthere may be several different sources of determinate error, eachsource has a specific magnitude and sign. Some sources of determinate errorare positive and others are negative, and some are larger in magnitude andothers are smaller. The cumulative effect of these determinate errors is a netpositive or negative error in accuracy.We assign determinate errors into four categories—sampling errors,method errors, measurement errors, and personal errors—each of whichwe consider in this section.Sa m p l i n g Er r o r sA determinate sampling error occurs when our sampling strategy doesnot provide a representative sample. For example, if you monitor the envi-