Definition · Plain-language
Alternative hypothesis
An alternative hypothesis (H1 or Ha) is the statement that there is an effect, difference, or relationship between variables — the outcome a researcher expects and sets out to support.
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The statement of an effect
The alternative hypothesis, written H1 or Ha, is the proposition that something is going on: a treatment changes an outcome, two groups differ, or two variables are related. It is the mirror image of the null hypothesis and usually captures what the researcher genuinely expects or hopes to demonstrate. For a trial comparing a drug with a placebo, the alternative might state that mean recovery time differs between the two groups. Because the alternative carries the substantive prediction, it is what a study is ultimately trying to find evidence for.
Directional or non-directional
An alternative hypothesis can be non-directional (two-tailed), simply asserting that a difference or relationship exists without specifying its direction, or directional (one-tailed), predicting which way the effect runs — for example that a new teaching method raises scores rather than merely changing them. Directional alternatives are appropriate when theory or prior evidence justifies a specific prediction, and they concentrate statistical power in that direction; non-directional alternatives are the safer default when the direction is genuinely uncertain. The choice should be made and recorded before data are collected.
How it relates to the null
The alternative and null hypotheses are mutually exclusive and jointly exhaustive: between them they cover every possibility for the parameter being tested. Hypothesis testing never tries to confirm the alternative directly. Instead it asks whether the evidence is strong enough to reject the null; if it is, that rejection is taken as support for the alternative. This indirect route is why results are reported as "the null was rejected" rather than "the alternative was proven", and why preregistering the alternative in advance helps keep the test honest.
Key facts
At a glance
- Definition: statement that an effect, difference or relationship exists
- Symbol: H1 or Ha
- Role: the prediction the researcher expects to support
- Tested against: the null hypothesis (H0) of no effect
- Forms: directional (one-tailed) or non-directional (two-tailed)
- Why it matters: carries the study’s substantive claim about the variables
Common misconceptions
What people often get wrong
Often heard: A statistical test directly proves the alternative hypothesis.
Actually: Tests assess the null, not the alternative. You reject the null when evidence is strong, and that rejection is read as support for the alternative — the alternative is never proven outright.
Often heard: The alternative hypothesis must always predict a direction.
Actually: It can be non-directional, asserting only that a difference or relationship exists. Directional (one-tailed) alternatives require prior justification and should be specified before data collection.
Often heard: The alternative and null hypotheses are independent guesses you can pick freely.
Actually: They are tightly linked: mutually exclusive and jointly exhaustive. The alternative is precisely the complement of the null for the parameter being tested.
Going deeper
