A statistically significant result means the observed data would be unlikely if the null hypothesis were true.

Is it true that a statistically significant result means the observed data would be unlikely if the null hypothesis were true?

Yes. Two reference sources state directly that a statistically significant result means the observed data would be unlikely under the null hypothesis, and a statistics Q&A gives the same conditional probability (rejecting a true null 5% of the time at alpha = 0.05). Two further sources only gesture at the idea by linking smaller p-values to stronger evidence against the null.

Verdict: SUPPORTED · 5 sources for, 0 against · Last checked 3 Oct 2026

The private library was unavailable for some searches in this check. Missing library results are not evidence against the claim.

Statistical hypothesis test. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/Statistical_hypothesis_test

statistically significant. (n.d.). cancer.gov. https://www.cancer.gov/publications/dictionaries/cancer-terms/def/statistically-significant

P – VALUE, A TRUE TEST OF STATISTICAL SIGNIFICANCE? A CAUTIONARY NOTE - PMC Lock. (n.d.). pmc.ncbi.nlm.nih.gov. https://doi.org/10.4314/aipm.v6i1.64038

what does For a significance threshold of 0.05, if the null hypothesis is true mean. (2020). stats.stackexchange.com. https://stats.stackexchange.com/questions/502071/what-does-for-a-significance-threshold-of-0-05-if-the-null-hypothesis-is-true-m

p-value - Wikipedia. (n.d.). en.wikipedia.org. https://en.wikipedia.org/wiki/P-value