Updated June 17, 2026
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A p-value is the probability of getting a result as extreme as the one you observed, assuming the null hypothesis (no effect, no difference) is true. A small p-value means your data would be unusual if there were no real effect, so you have grounds to reject the null hypothesis.
What the null hypothesis is
Every hypothesis test starts with a null hypothesis (H0) that says nothing is happening: no difference between groups, no relationship between variables, or the effect is zero. The p-value tells you how likely your data is under that assumption of nothing. If the data looks very unlikely under H0, you reject H0 in favor of your alternative hypothesis (H1).
What does p less than 0.05 mean?
A threshold of 0.05 is the most common cutoff in social science and medicine. It means: if the null were true, you would see a result this extreme only 5% of the time by chance. Crossing that line does not prove your hypothesis; it means the data is inconsistent enough with H0 to reject it at a 5% error rate. You are accepting a 5% chance of a false positive (Type I error).
| p-value | Conventional interpretation |
|---|---|
| p < 0.001 | Very strong evidence against null |
| 0.001 to 0.01 | Strong evidence |
| 0.01 to 0.05 | Moderate evidence; commonly called "significant" |
| 0.05 to 0.10 | Weak evidence; sometimes called "marginal" |
| p > 0.10 | Little or no evidence against null |
Worked example
You test whether a new drug lowers blood pressure. The mean drop in the treatment group is 8 mmHg; in the control group it is 2 mmHg. You compute a t-test and get p = 0.03. Interpretation: if there were truly no drug effect, you would see a difference this large only 3% of the time by chance. At the 0.05 threshold, you reject the null and conclude the drug likely has a real effect. Use the p-value calculator to get the exact figure from your test statistic.
What p = 0.75 means
A p-value of 0.75 is not significant. It means your data is entirely consistent with the null hypothesis; there is no reason from this evidence to conclude an effect exists. A high p-value does not prove the null is true, but it does mean you failed to find evidence against it.
Common mistakes
The most important mistake is treating p < 0.05 as proof of a real effect. It only controls the false-positive rate; it says nothing about effect size or practical importance. A tiny, meaningless difference can produce p < 0.05 with a large enough sample. Always pair your p-value with a confidence interval and an effect-size measure to get the full picture.
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