Clinical Trials

Clinical Trials: A Practical Guide ■❚❙❘Figure 1. Three t-distributions and their relationship with a standard normal distribution.4df = 1df = 5df = 25normal3Density210–4 –2 024tdf = degrees of freedom.standard normal distribution. Figure 1 displays three t-distributions with degreesof freedom of 1, 5, and 25, and the standard normal distribution. We can see thatas the number of degrees of freedom increases, the t-distribution approachesthe standard normal distribution. Therefore, as the degrees of freedom increases,the t-distribution moves towards the normal distribution and the Z-test introducedin Chapter 18 can be used for hypothesis testing, rather than the t-test.Critical valuesThe principles for a significance test are as described in Chapter 18. For theone-sample t-test, if:|t| ≥ t α/2,n–1where t α/2,n–1is a critical value of a t-distribution with n – 1 degrees of freedom, wewould have evidence against the null hypothesis that μ = μ 0, ie, the populationmean (μ) is statistically significantly different from the constant μ 0at the α levelof significance.201