Understanding statistical hypothesis tests and power

Medical researchers often attempt to understand whether a risk factor is involved in the aetiology of disease or whether an intervention reduces disease; this has been the subject of another article in this series.1 We typically do this by proposing scientific hypotheses from which testable statistical hypotheses can be developed. For example, our scientific hypothesis could be that people with irritable bowel syndrome (IBS) have higher risk of depression compared with those who do not have IBS. A small study might show that one in ten in the control group have depression, compared with two in ten in the IBS group. This might reflect a real difference in the rate of depression between IBS and non-IBS populations, or the difference of one person between groups might simply be the play of chance. An empirical approach to answering this question might be to repeat the study multiple times, with larger numbers, and to look at the consistency of the results. Unfortunately, this is an expensive and time-consuming solution.