Analytical Chem istry - DePauw University

112 Analytical Chemistry 2.0difference between the methods if we use different patients to gather datafor each method. Using paired data, in which the we analyze each patient’sblood using both methods, prevents a large variance within a populationfrom adversely affecting a t-test of means.When using paired data we first calculate the difference, d i , betweenthe paired values for each sample. Using these difference values, we thencalculate the average difference, d , and the standard deviation of the differences,s d . The null hypothesis, H : d = 0 , is that there is no difference0between the two samples, and the alternative hypothesis, H : d ≠ 0 , isAthat the difference between the two samples is significant.The test statistic, t exp , is derived from a confidence interval around dtexp =ds dnwhere n is the number of paired samples. As is true for other forms of thet-test, we compare t exp to t(a,n), where the degrees of freedom, n, is n – 1.If t exp is greater than t(a,n), then we reject the null hypothesis and acceptthe alternative hypothesis. We retain the null hypothesis if t exp is less thanor equal to t(a,n). This is known as a paired t-test.Example 4.21Marecek et. al. developed a new electrochemical method for rapidly determiningthe concentration of the antibiotic monensin in fermentation vats. 7The standard method for the analysis, a test for microbiological activity,is both difficult and time consuming. Samples were collected from thefermentation vats at various times during production and analyzed for theconcentration of monensin using both methods. The results, in parts perthousand (ppt), are reported in the following table.Sample Microbiological Electrochemical1 129.5 132.32 89.6 91.03 76.6 73.64 52.2 58.25 110.8 104.26 50.4 49.97 72.4 82.18 141.4 154.19 75.0 73.410 34.1 38.111 60.3 60.17 Marecek, V.; Janchenova, H.; Brezina, M.; Betti, M. Anal. Chim. Acta 1991, 244, 15–19.