Introduction
This topic covers the logic of statistical hypothesis testing: how a research question is turned into testable hypotheses, how the p-value and the level of significance are used to decide between them, what statistical power means, and the two kinds of error a decision can produce. It is the foundation for the tests in topics 25 to 27.
Hypotheses
Every study starts with a question that is first written as a clear scientific claim and then translated into two statistical statements that can be tested against data.
- Working hypothesis: the research question expressed as a claim, for example that a new drug lowers systolic pressure more than placebo. It is formulated before data are analysed.
- Null hypothesis (H0): the statement of no difference, no association or no effect. It is the hypothesis that is tested directly.
- Alternative hypothesis (H1): the claim that there is a difference or an effect. It can be two-sided (the groups differ, in either direction) or one-sided (one group is greater or smaller). A one-sided alternative must be justified before the data are collected.
A test never proves the alternative hypothesis. It only leads either to rejecting H0 or to failing to reject it. Failing to reject H0 does not show that H0 is true.