Clinical Trials

❘❙❚■ Chapter 18 | Significance Tests and Confidence IntervalsThis statistic follows a normal standard distribution under the null hypothesis [2,3].For the SBP data:• X = 130 mm Hg• S = 10 mm Hg• n = 500• μ 0= 129 mm HgReplacing the values in the formula generates Z = 2.24.A variety of statistical methods can be used to address different study questions(eg, comparing treatment difference in means and proportions), and we willintroduce a number of standard statistical methods in later chapters. Thechoice of statistical test will depend on the types of data and hypotheses underquestion [2,3].Step 3: Specify a significance level and determine its critical valuesaccording to the distribution of the test statisticHaving obtained the appropriate test statistic (in our example, the Z-value), thenext step is to specify a significance level. This is a fixed probability of wronglyrejecting the null hypothesis, H 0, if it is in fact true. This probability is chosen bythe investigators, taking into account the consequences of such an error [2,3].That is, the significance level is kept low in order to reduce the chance ofinadvertently making a false claim. The significance level, denoted by α, is usuallychosen to be 0.05 (5%), but can sometimes be set at 0.01.Figure 2 graphically displays the α of a two-sided Z-test under the null hypothesis,ie, the area under the normal distribution curve below –Z α/2and above Z α/2.The corresponding Z α/2is called the critical value of the Z-test. The critical valuefor a hypothesis test is a threshold with which the value of the test statistic calculatedfrom a sample is compared in order to determine the P-value to be introduced inthe next step.From Figure 2, we see that a two-sided Z-test has an equal chance of showing thatμ (mean SBP of adult males in our sample) is bigger than μ 0on one side (aboveZ α/2) or smaller than μ 0(below –Z α/2) on the other side if the null hypothesis is true.The area under the curve below –Z α/2and above Z α/2is known as the null hypothesisrejection region. If the Z-value falls within this region then the null hypothesis isrejected at the α level.• If α = 0.05, we have Z 0.05/2= 1.96.• If α = 0.01, we have Z 0.01/2= 2.58.188