Analytical Chem istry - DePauw University

Chapter 4 Evaluating Analytical Data149Example 4.20F-Test Two-Sample for VariancesPractice Exercise 4.13Shown here are copies of R sessions for each problem. You will find smalldifferences between the values given here for t exp and F exp , and for thosevalues shown with the worked solutions in the chapter. These differencesarise because R does not round off the results of intermediate calculations.Example 4.20Analyst A Analyst B86.82 81.0187.04 86.1586.93 81.7387.01 83.1986.20 80.2787.00 83.94t-Test: Two-Sample Assuming Unequal VariancesAnalyst A Analyst BMean 86.8333333 82.715Variance 0.10246667 4.67615Observations 6 6Hypothesized Mean Difference 0df 5t Stat 4.6147271P(T AnalystB=c(81.01, 86.15, 81.73, 83.19, 80.27, 83.94)> var.test(AnalystB, AnalystA)F test to compare two variancesdata: AnalystB and AnalystAF = 45.6358, num df = 5, denom df = 5, p-value = 0.0007148alternative hypothesis: true ratio of variances is not equal to 195 percent confidence interval:6.385863 326.130970sample estimates:ratio of variances45.63582> t.test(AnalystA, AnalystB, var.equal=FALSE)Example 4.21Microbiological Electrochemical129.5 132.389.6 91.076.6 73.652.2 58.2110.8 104.250.4 49.972.4 82.1141.4 154.175.0 73.434.1 38.160.3 60.1Analyst B Analyst AMean 82.715 86.8333333Variancedf4.6761550.102466675ObservationsF645.63581656t-Test: Paired Two Sample for MeansMicrobiologicalP(F