In simple terms
Statistical significance is a check on whether a pattern in data could plausibly be a fluke.
Researchers start from a null hypothesis, the assumption that there is no real effect. They then ask how surprising their data would be if that assumption were true.
How it works
The answer arrives as a p-value: the probability, under a specified statistical model, that a summary of the data would be equal to or more extreme than the value actually observed.
A threshold is fixed in advance, called the significance level, or alpha. Alpha is the risk of rejecting the null hypothesis when it is in fact true, known as an error of the first kind. Failing to reject a null hypothesis that is false is an error of the second kind.
If the p-value falls below alpha, the result is called statistically significant. Many fields settle on 0.05 by convention, but that number is a choice, not a property of nature.
Why it matters
The label carries weight it was never designed to carry. It shapes what gets published, funded and reported.
The American Statistical Association has said so directly. A p-value does not measure the probability that the studied hypothesis is true, nor the probability that the data arose by chance alone. It does not measure the size of an effect or the importance of a result. And scientific conclusions and policy decisions, the ASA says, should not rest on whether a p-value clears a threshold.
Two practical consequences follow. A significant result can be real but far too small to matter. A result that misses the threshold is not evidence that nothing is there.
Where you’ll see it
- Clinical trial results and medicine approvals.
- Papers reporting p less than 0.05, or not significant.
- News coverage saying a study proved something.
Example
A trial reports a p-value of 0.03. With alpha set at 0.05, the result counts as statistically significant. That says the data sit awkwardly with the no-effect model. It says nothing about how large the effect is.
Often confused with
Practical significance. Statistical significance asks whether an effect can be told apart from chance. Practical significance asks whether it is large enough to matter.
Key facts
- The ASA defines a p-value as the probability under a specified statistical model that a statistical summary of the data would be equal to or more extreme than its observed value.1
- ASA principle 2: p-values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone.1
- ASA principle 3: scientific conclusions and business or policy decisions should not be based only on whether a p-value passes a specific threshold.1
- ASA principle 5: a p-value, or statistical significance, does not measure the size of an effect or the importance of a result.1
- The significance level alpha is the risk of rejecting the null hypothesis when it is in fact true; the risk of failing to reject a false null hypothesis is the error of the second kind.2
Related concepts
In the news
Quick checkDoes a statistically significant result tell you the effect is large?Show answer
No. The ASA states that a p-value does not measure the size of an effect or the importance of a result.
Sources
- American Statistical Association (Ronald L. Wasserstein and Nicole A. Lazar). The ASA Statement on p-Values: Context, Process, and Purpose. 9 June 2016 (accessed 14 September 2026)
- NIST/SEMATECH. e-Handbook of Statistical Methods, section 7.1.3: What are statistical tests?. Undated (accessed 14 September 2026)
Editorially reviewed by Specialty Digest Editorial TeamLast reviewed September 17, 2026Researched and drafted with AI assistanceReport an issue