Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Figure 2. Null hypothesis rejection regions (shaded areas) of two-sided Z-test.| | |–Z α/20 Z α/2Step 4: Determine a P-value by comparing the value of the teststatistic with the critical valueA P-value is the probability of our result (Z = 2.24 for the SBP data) or a moreextreme result (Z ≤ –2.24 or Z > 2.24) being observed, assuming that the nullhypothesis is true. The exact P-value in the Z-test is the probability of Z ≤ –Z α/2orZ ≥ Z α/2, which can always be determined by calculating the area under the curvein two-sided symmetric tails from a statistical table, specifically of a normaldistribution (see Chapter 17) [3]. For the SBP data, the exact P-value is 0.025.In a practical application, we often need to determine whether the P-value issmaller than a specified significance level, α. This is done by comparing the valueof the test statistic with the critical value. It can be seen from Figure 2 that P ≤ αif, and only if:• Z ≤ –Z α/2; or• Z ≥ Z α/2For the SBP data, since Z = 2.24 > Z 0.05/2= 1.96, we can conclude that P < 0.05.It can be seen from Figure 2 that a smaller P-value indicates that Z is further awayfrom the center (ie, the null value μ – μ 0= 0), and consequently provides strongerevidence to support the alternative hypothesis of a difference.189