Clinical Trials

❘❙❚■ Chapter 19 | Comparison of MeansTable 7. Summary of statistical test methods described in this article.Type of tests Null hypothesis Test statistics and confidence interval AssumptionsOne-sample t-test H 0: μ = μ 0Sample is from at = X – μ 0,df = n – 1SE(X)normal distributionSE(X) = S / √nCI: X ± t α/2,n–1× SE(X)Paired t-test H 0: μ d= μ pre– μ post= 0 Xt = d ,df = n – 1The paired populationSE(X d)differences arenormally distributedSE(X d) = S d/ √nCI: X d± t α/2,n–1× SE(X d)Two-sample t-test H 0: μ 1= μ X2For the two populationst = 1– X 2 ,df = n1 + n 2– 2SE(X 1– X 2)(eg, all patients toreceive treatment ASE(X 1– X 2) =and B):2[n • the two samples1– 1]S 12+ [n 2– 1]S 2[ 1 + 1 ] are independent(1 /2n 1+ n 2– 2 n 1n ) 2• the two samplesare from twoCI: (X 1– X 2) ± t × SE(X – X )α/2,n1 +n 2 –2 1 2normal populations• the variances ofthe two populationsare equal• the two populationsare homogeneous interms of observedand unobservedcharacteristicsat baselineTwo-sample Z-test H 0: μ 1= μ 2X • The two samplesZ = 1– X 2SE(Xare independent1– X 2)• The two samplesare from twoSE(X 1– X 2) = S 21+ normal populations( S 2 1 /22n 1n ) 2• The samples havelarge sizesCI: (X 1– X 2) ± Z α/2× SE(X 1– X 2)• The two populationsare homogeneous interms of observedand unobservedcharacteristicsat baselinenWilcoxon rank-sum The two samples1The two samples(Mann–Whitney) test are drawn from T = ΣR 1iare independenti = 1a single populationμ T= n 1(n 1+ n 2+ 1) / 2σ T= √n 1n 2(n 1+ n 2+ 1) / 12Z = (T – μ T) / σ T214