Clinical Trials

❘❙❚■ Chapter 18 | Significance Tests and Confidence IntervalsTable 2. Type I and II errors in hypothesis testing.If H 0: μ 1= μ 2is:Statistical inference True FalseReject H 0: Type I error (α) Correctsignificant difference‘Consumer’s risk’Retain H 0: Correct Type II error (β)nonsignificant difference‘Manufacturer’s risk’In addition, we might want to provide some measure of our uncertainty as to howclose the sample mean is to the true population mean. This is done by calculatinga CI (or interval estimate) – a range of values that has a specified probability ofcontaining the true population parameter being estimated. For example, a 95% CIfor the mean is usually interpreted as a range of values containing the truepopulation mean with a probability of 0.95 [2]. The formula for the (1 – α)% CIaround the sample mean (X) corresponding to the Z-test, is given by:X ± Z α/2SE(X)where SE(X) is the standard error of X, calculated by S / √n. This is a measure ofthe uncertainty of a single sample mean (X) as an estimate of the populationmean [2]. This uncertainty decreases as the sample size increases. The larger thesample size, the smaller the standard error – therefore the narrower the interval,the more precise the point estimate.For our SBP example, the 95% CI for the population mean (μ) can be calculatedwith the following formula:X ± 1.96S / √n = 129.1 to 130.9 mm HgThis means that the interval between 129.1 and 130.9 mm Hg has a 0.95 probabilityof containing the population mean μ. In other words, we are 95% confident thatthe true population mean is between 129.1 and 130.9 mm Hg, with the bestestimate being 130 mm Hg.CIs can be calculated not just for a mean, but also for any estimated parameterdepending on the data types and statistical methods used (see references [2,3]for more). For example, you could estimate the proportion of people who smokein a population, or the difference between the mean SBP in subjects taking anantihypertensive drug and those taking a placebo.192