In simple terms
A p-value is a number that says how surprising your data would be if nothing were really going on.
The American Statistical Association puts it carefully: a p-value can indicate how incompatible the data are with a specified statistical model.
How it works
Researchers start from a null hypothesis, the assumption of no effect or no difference. They then calculate a test statistic from the data they collected.
NIST defines the p-value as the probability of the test statistic being at least as extreme as the one observed, given that the null hypothesis is true. A small p-value means such data would be unusual under that assumption.
A threshold, written as alpha, is chosen before the test. NIST describes alpha as the risk of rejecting the null hypothesis when it is in fact true, with 0.01, 0.05 and 0.10 as common choices.
Tightening alpha trades one error for another. NIST notes that as alpha falls, the risk of failing to detect a real effect rises.
Why it matters
P-values help decide what gets published, funded and reported as a finding, which is why their limits are argued over so loudly.
The 2016 ASA statement is blunt. P-values do not measure the probability that the studied hypothesis is true. A p-value, or statistical significance, does not measure the size of an effect or the importance of a result. The ASA also warns against basing scientific conclusions or policy decisions on whether a p-value clears a threshold.
Where you will see it
- Results tables in medical, social science and economics papers.
- Drug trial readouts, usually printed beside a confidence interval.
- Journal policies and reporting standards for statistical claims.
- Debates about the replication crisis and preregistration.
Example
A trial reports p = 0.03 for a difference between two groups. That says the data would be fairly unusual if the treatments were truly identical. It does not say the difference is large, nor that there is a 97 percent chance the treatment works.
Often confused with
Statistical significance is a verdict reached by comparing a p-value with a chosen threshold. The p-value itself is the continuous measure sitting behind that verdict.
Key facts
- The ASA states that p-values can indicate how incompatible the data are with a specified statistical model.1
- The 2016 ASA statement says p-values do not measure the probability that the studied hypothesis is true.1
- The ASA states that a p-value, or statistical significance, does not measure the size of an effect or the importance of a result.1
- NIST defines the p-value as the probability of the test statistic being at least as extreme as the one observed, given that the null hypothesis is true.2
- NIST describes the significance level alpha as the risk of rejecting a true null hypothesis, with 0.01, 0.05 and 0.10 as common choices.2
Related concepts
In the news
Quick checkDoes a p-value tell you the probability that your hypothesis is true?Show answer
No. It measures how incompatible the data are with a specified model, usually one assuming no effect.
Sources
- American Statistical Association. ASA Statement on Statistical Significance and P-Values. 2016 (accessed 23 September 2026)
- NIST and SEMATECH. e-Handbook of Statistical Methods, Chapter 7: Product and Process Comparisons. Undated (accessed 23 September 2026)
Editorially reviewed by Specialty Digest Editorial TeamLast reviewed September 23, 2026Researched and drafted with AI assistanceReport an issue