Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘For illustrative purposes, we will focus on the Wilcoxon rank-sum test forcomparing two independent treatment groups.The null hypothesis in the Wilcoxon rank-sum test is that the two samples aredrawn from a single population. The test involves the calculation of a statistic,usually called T, whose distribution under the null hypothesis is unknown. TheWilcoxon method requires all the observations to be ranked as if they were froma single population. If the data are tied or equal, then averaged ranks across tiedvalues are used (see Table 6). Wilcoxon’s test statistic is the sum of the ranks forthe observations in the first sample [7–9]:n 1T 1= Σ R 1i = 1With this Wilcoxon’s test statistic, we can find the corresponding exact P-valuefrom a statistical table [7–9]. However, we will illustrate how the P-value canbe obtained from an alternative approximate Z-test, whose working can bereadily examined.When the sample size in each group is large, the statistic T 1has an approximatelynormal distribution with:mean μ r= √n 1(n 1+ n 2+ 2) / 2standard deviation σ T= n 1n 2(n 1+ n 2+ 1) / 12From these, we can calculate the test statistic Z as (T 1– μ r) / σ rand refer to thestandard normal distribution table for determining the P-value.Table 5 shows the data of relative change in FEV 1treated in this way. The sums ofthe ranks in the two treatment groups are 211 and 89, respectively. So we haveT 1= 211. The mean and standard deviation of the test statistic under the nullhypothesis are given by:μ r= 12 * (12 + 12 + 1) / 2 = 150andσ T= √12 * 12(12 + 12 + 1) / 12 = 17.32yielding:Z = 211 – 150 = 3.5217.32211