Reject the null hypothesis

How it is used

The standard way to state a test decision. Its opposite is 'fail to reject the null hypothesis' (or 'retain' it), never 'accept' or 'prove' it, because absence of evidence is not evidence of absence. Exam answers are expected to use exactly these words.

Example sentences

1. Since p = .002, we reject the null hypothesis of equal means.

2. At α = 0.05 we cannot reject the null hypothesis, so the data show no clear difference between the two suppliers.

Common collocations

• fail to reject the null hypothesis
• reject H₀ at the 5% level
• the decision to reject
• grounds to reject

Related terms

• null hypothesisThe default claim in a statistical test that there is no effect, no difference or no relationship; the test checks whether the data give enough evidence against it.
• p-valueThe probability of getting a result at least as extreme as the one observed if the null hypothesis were true; a small value means the data would be surprising under the null.
• significance levelThe threshold, chosen before a test, below which a p-value is treated as statistically significant; it is also the accepted risk of a Type I error.
• type I errorRejecting a null hypothesis that is actually true, in other words concluding that an effect exists when it does not; a false positive.
• alternative hypothesisThe statement that there is a real effect, difference or relationship; it is the claim a researcher usually expects, and the data support it when they give strong evidence against the null hypothesis.

More terms: Hypothesis Testing

• hypothesis
• statistical significance
• t-test
• chi-square test
• ANOVA
• type II error
• statistical power
• degrees of freedom
• two-tailed test
• assumption
• nonparametric test
• post hoc test