Clinical Trials

❘❙❚■ Chapter 19 | Comparison of MeansTable 6. Calculation of ranks of relative changes for the Wilcoxon rank-sum test.Subject Treatment Relative change (%) Rank of relative changeTreatment ATreatment B1 B 12.5 112 B –4.5 43 B –12.5 14 A 23.3 20.55 B –0.3 56 A 33.0 237 A 19.3 168 B 18.1 14.59 B –11.2 210 A 14.5 1211 A 12.3 1012 A 42.5 2413 B 9.4 814 B 9.6 915 B 21.4 18.516 A 30.3 2217 B 8.4 718 A 17.1 1319 A 21.4 18.520 B –8.1 321 B 5.0 622 A 23.3 20.523 A 20.8 1724 A 18.1 14.5Sum of ranks T 1= 211 T 2= 89which, from the standard normal distribution table, corresponds to P = 0.0004.Since P < 0.05, there is evidence against the null hypothesis that the two samplesare drawn from a single population at the 5% significance level. As the medianrelative change in FEV 1for the active treatment group is 21.1%, much higher than6.7% in the placebo group, we can conclude that there is strong evidence tosuggest that the active drug increases FEV 1.Thus, we can see that using ranking to assess whether the changes are really equalin both groups allows us to determine whether the two groups are drawn from thesame population.212