Hypothesis testing is a statistical method for evaluating whether sample evidence is inconsistent with a specified null hypothesis. Understanding the logic is more important than memorizing a sequence of formulas.
Define the hypotheses
The null hypothesis, usually written H₀, represents the claim evaluated by the test. The alternative hypothesis, H₁ or Hₐ, represents the competing claim.
For example, a researcher may test whether a population mean differs from a stated reference value. The exact hypotheses depend on the research question.
Choose a significance level
The significance level, often written α, is a threshold selected before examining the test result. A common choice is 0.05, but the appropriate level depends on the context and consequences of errors.
Understand the p-value
A p-value is the probability, assuming the null hypothesis and the test assumptions are true, of obtaining a result at least as extreme as the one observed.
A p-value is not the probability that the null hypothesis is true. It also does not measure the size or practical importance of an effect.
Make a decision carefully
In a conventional test, a p-value at or below the selected significance level leads to rejection of the null hypothesis. Otherwise, the result is described as failing to reject it.
Failing to reject the null hypothesis does not prove that it is true. Interpret the result alongside the study design, assumptions, effect size and uncertainty.
Common mistakes to avoid
Do not confuse statistical significance with practical significance, or treat one p-value as the whole story. Report the method and assumptions clearly and explain what the result means in context.
Understanding the concept is the first step.
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