Hypothesis test

A hypothesis test evaluates whether the observed data are sufficiently incompatible with a baseline claim to warrant rejecting it under a specified statistical model.

Core idea

The procedure starts with two competing statements:

• The null hypothesis $H_0$ is the baseline statement tested against the data.
• The alternative hypothesis $H_a$ represents the competing statement.

The data are summarized through a test statistic, and that statistic is evaluated relative to what would be expected if $H_0$ were true.

What a test requires

1. A clearly stated null and alternative hypothesis.
2. A sampling model and assumptions.
3. A test statistic that captures the relevant departure from the null model.
4. A rule for interpretation, such as a critical region, p-value, or interval-based decision framework.

What it does well

Hypothesis tests are useful when the scientific question is framed as a specific incompatibility claim, for example whether a mean difference is plausibly zero or whether an observed association is stronger than expected by chance under a reference model.

Common limitation

A hypothesis test does not measure the size, relevance, or practical importance of an effect. It is only one part of inference and is often most informative when combined with effect sizes, uncertainty intervals, and model comparison.

See also: test statistic, Hypothesis testing, information criteria, Statistical inference, MOC Projects and Research Threads