The null hypothesis
A typical research question is most easily expressed in terms of there being some difference between groups. For example, 'In patients with acute myocardial infarction (AMI), does the administration of intravenous nitrate (as compared with none) reduce mortality?' To answer this question, the most appropriate study design would be a randomized controlled trial comparing AMI patients who receive intravenous nitrate with control patients. The challenge then is to interpret the results of that study. Even if there is no real effect of intravenous nitrate on mortality, sampling variation means that it is extremely unlikely that exactly the same proportion of patients in each group will die. Thus, any observed difference between the two groups may be due to the treatment or it may simply be a coincidence, in other words due to chance. The aim of hypothesis testing is to establish which of these explanations is most likely. Note that statistical analyses can never prove the truth of a hypothesis, but rather merely provide evidence to support or refute it.
To do this, the research question is more formally expressed in terms of there being no difference. This is known as the null hypothesis. In the current example the null hypothesis would be expressed as, 'The administration of intravenous nitrate has no effect on mortality in AMI patients.'
In hypothesis testing any observed differences between two (or more) groups are interpreted within the context of this null hypothesis. More formally, hypothesis testing explores how likely it is that the observed difference would be seen by chance alone if the null hypothesis were true.