Definition · Plain-language
Null hypothesis
A null hypothesis (H0) is the default position in hypothesis testing: a statement that there is no effect, no difference, or no relationship between the variables being studied.
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The default statement of no effect
The null hypothesis, written H0, expresses the position that nothing is going on: the treatment makes no difference, the groups do not differ, or two variables are unrelated. It is deliberately the dull, conservative claim — the baseline a study assumes until the data give good reason to think otherwise. For a trial comparing a drug with a placebo, the null might state that the mean recovery time is the same in both groups. By framing the default as "no effect", researchers force the evidence, rather than their hopes, to do the work of overturning it.
How it pairs with the alternative hypothesis
A null hypothesis is always tested against an alternative hypothesis (H1 or Ha), which states the effect, difference, or relationship the researcher actually expects to find. The two are mutually exclusive and together cover the possibilities: if the evidence is strong enough to reject H0, support shifts to Ha. Phrasing the pair clearly before collecting data is part of good practice and underpins preregistration, where hypotheses are recorded in advance to guard against shifting the goalposts once results are in.
You reject it, you never prove it
Hypothesis testing assesses whether the observed evidence is strong enough to reject the null — not whether the null is true. When a result is statistically significant, you reject H0; when it is not, you fail to reject it. Crucially, failing to reject the null is not the same as proving it: absence of evidence for an effect is not evidence that no effect exists. This asymmetry mirrors the logic of falsification — a claim earns credibility by surviving attempts to refute it, never by being conclusively confirmed.
Key facts
At a glance
- Definition: statement of no effect, no difference or no relationship between variables
- Symbol: H0 (pronounced "H-nought" or "H-zero")
- Role: the default the test is designed to challenge
- Paired with: the alternative hypothesis (H1 / Ha)
- Outcome: you reject it or fail to reject it — never "prove" it
- Why it matters: gives hypothesis testing an objective, falsifiable baseline
Common misconceptions
What people often get wrong
Often heard: The null hypothesis is the result the researcher hopes to confirm.
Actually: It is the opposite. The null states no effect or no difference — the baseline a researcher usually hopes to reject in favour of the alternative hypothesis, which carries the expected effect.
Often heard: A non-significant result proves the null hypothesis is true.
Actually: It does not. Failing to reject H0 means the evidence was too weak to overturn it, not that no effect exists. Absence of evidence is not evidence of absence.
Often heard: You can directly prove the null hypothesis with enough data.
Actually: Hypothesis testing is asymmetric: you can reject the null or fail to reject it, but never conclusively prove it. The logic mirrors falsification rather than verification.
Going deeper
