P-Value Calculator
Get the p-value from a z, t or χ² test statistic – one- or two-tailed – and see whether the result is significant at your chosen α.
What the p-value means
The p-value is the probability of a result at least as extreme as yours if the null hypothesis H₀ were true. A small p-value means your data would be surprising under H₀. If p is below the significance level α – usually 0.05 – the result is called statistically significant and H₀ is rejected.
Examples
- z = 2.1, two-tailed: p = 2 × (1 − Φ(2.1)) = 0.0357 – significant at 0.05.
- t = 2.1 with 15 degrees of freedom, two-tailed: p = 0.0531 – just not significant. The t distribution has heavier tails, so the same statistic gives a larger p.
- χ² = 18.3 with 10 degrees of freedom: p = 0.0501.
One- or two-tailed?
Use two-tailed when any difference counts (the new method could be better or worse). Use one-tailed only when the hypothesis predicts a direction before you see the data. The two-tailed p-value is twice the one-tailed one.
Common mistakes
- p is not the probability that H₀ is true.
- p = 0.06 does not prove H₀ – it only says the data are not strong enough to reject it.
- A tiny p-value with a huge sample can come from an effect too small to matter. Report the effect size and a confidence interval too.
Frequently asked questions
What does p = 0.05 mean?
If H₀ were true, a result at least this extreme would occur 5% of the time.
What is the p-value for z = 1.96?
0.05 two-tailed, 0.025 one-tailed.