Almost every statistical test you run — a t-test, ANOVA, chi-square, correlation — hands you back a p-value. It's also the number people get wrong most often. This guide gives you a correct, intuitive understanding you can actually rely on.
Quick answers: what does my p-value mean?
Read against the usual threshold α = 0.05, where a result counts as significant when p ≤ α:
| Your p-value | Significant at 0.05? | What it means |
|---|---|---|
| p < 0.001 | Yes | Very strong evidence against the null hypothesis (often marked ***) |
| p = 0.01 | Yes | If there were no real effect, a result this extreme would happen only 1% of the time |
| p = 0.049 | Yes, just | Technically significant, but almost the same evidence as p = 0.051 — don’t overinterpret the cut-off |
| p = 0.05 | Borderline | Exactly on the threshold: it counts under the usual “p ≤ α” rule, but it is weak evidence |
| p = 0.06–0.10 | No | Sometimes called “marginal”: weak evidence; some fields flag p < 0.10 |
| p ≥ 0.05 (e.g. 0.30) | No | The data are consistent with no effect — but this is not proof that there is no effect |
Significance stars (*, **, ***)
Tables often mark p-values with stars. The most common convention is * p < 0.05, ** p < 0.01, *** p < 0.001. Many economics and regression tables use a shifted scale, written in the table note as *** p < 0.01, ** p < 0.05, * p < 0.10. The same number of stars can therefore mean different things, so always read the note under the table. Running many tests? Adjust the p-values with the multiple-comparisons calculator.
What a p-value actually is
A p-value answers one specific question:
"If there were truly no effect, how surprising would my data be?"
More precisely: the p-value is the probability of seeing a result at least as extreme as yours, assuming the null hypothesis is true (i.e. assuming there's really no difference or no relationship). A small p-value means your data would be very unlikely if nothing were going on — so something probably is going on.
Example: you compare two groups and get p = 0.02. That means: if the two groups were truly identical, you'd see a difference this big only about 2% of the time by random chance alone. That's unusual enough that most researchers conclude the groups genuinely differ.
Why 0.05?
The famous threshold — α = 0.05 — is a convention, not a law of nature. It means we're willing to be wrong 5% of the time (falsely declaring an effect when there isn't one). If p < 0.05, we call the result "statistically significant." Some fields use stricter thresholds (0.01 or lower) when false positives are costly. The number itself is a judgment call about acceptable risk.
| P-value | Usual interpretation |
|---|---|
| p < 0.01 | Strong evidence against the null |
| 0.01 – 0.05 | Moderate evidence; "significant" by convention |
| 0.05 – 0.10 | Weak / suggestive; not significant |
| p > 0.10 | Little to no evidence of an effect |
What a p-value is NOT
This is where most errors happen. A p-value is not:
- The probability that the null hypothesis is true. p = 0.02 does not mean "there's a 2% chance there's no effect." It's the probability of the data given the null, not the probability of the null given the data.
- The probability your result was due to chance. A close relative of the above misreading — still wrong.
- A measure of effect size. A tiny, unimportant difference can have a microscopic p-value if your sample is huge. See effect size.
- Proof of anything. p > 0.05 doesn't prove there's no effect — it just means you didn't find enough evidence for one.
Interpreting a significant result (p < 0.05)
You "reject the null hypothesis." In plain terms: your data provides enough evidence to conclude an effect or difference probably exists. But immediately ask two follow-up questions:
- How big is the effect? Report an effect size (Cohen's d, correlation r, etc.). Significance ≠ importance.
- What's the plausible range? A confidence interval tells you far more than a single p-value.
Interpreting a non-significant result (p > 0.05)
You "fail to reject the null." This is not the same as proving the null is true. Common reasons for a non-significant result include a genuinely tiny effect, but also simply too small a sample to detect a real effect. Before concluding "there's no difference," check whether your study had enough statistical power — an underpowered study fails to find effects that are really there.
The one-sentence summary: a p-value measures how surprising your data would be if nothing were going on — nothing more. Pair it with an effect size and a confidence interval, and you'll interpret results correctly every time.
Try it on your own data
Run a t-test and get an interpreted p-value →Enter your two groups; we return the p-value with a plain-English conclusion.Related reading: Choosing the right statistical test · Confidence intervals explained · Effect size explained.
See also: P-value calculator · How to calculate a p-value · P-hacking explained
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.