Clinical Trials

❘❙❚■ Chapter 18 | Significance Tests and Confidence IntervalsSample, population, and statistical inferenceSuppose that it is necessary to measure the average systolic blood pressure (SBP)level of all males aged ≥16 years in the UK in 2005. For practical and financialreasons, it is not possible to directly measure the SBP of every adult male in theUK; instead, we can conduct a survey among a subset (or ‘sample’) of 500 maleswithin this population. Through statistical inference, we can measure theproperties of the sample (such as the mean and standard deviation) and use thesevalues to infer the properties of the entire UK adult male population [1,2]. Thisprocess is illustrated in Figure 1.Population properties are usually determined by population parameters(numerical characteristics of a population) that are fixed and usually unknownquantities, such as the mean (μ) and standard deviation (σ) in a normaldistribution N(μ,σ 2 ) (see Chapter 17). [3]. The statistical properties of the sample,such as the mean (X) and standard deviation (S), can be used to provideestimates of the corresponding population parameters. Conventionally, Greekletters are used to refer to population parameters, while Roman letters refer tosample estimates.Two strategies that are often used to make statistical inference are [2,3]:• hypothesis testing• confidence intervals (CIs)These two methods are introduced below, illustrated with examples.Hypothesis testingStatistical inference can be made by performing a hypothesis (or significance) test,which involves a series of statistical calculations [3,4]. In the sample of 500 adultmales, the mean SBP (X) was 130 mm Hg, with a standard deviation (S) of10 mm Hg. The empirical estimate for the mean SBP of this population fromprevious medical literature is reported as 129 mm Hg (denoted by μ 0). So, we wantto know whether there is any evidence that the mean SBP value for all adult malesin the UK in 2005 (μ) is different from 129 mm Hg (μ 0).Step 1: Null and alternative hypothesesWe start by stating a hypothesis that the population mean SBP for all adult menin 2005 is 129 mm Hg, or μ = μ 0(ie, no different to that reported in the medicalliterature). This is referred to as the null hypothesis and is usually written as H 0,186