P-Value Calculator
Calculate the p-value from the test statistic (Z, t, chi², F) for one-tailed and two-tailed tests.
Tip: p < 0.05 doesn't mean 'the effect is large' — it only means 'the effect is statistically distinguishable from zero'. Also look at the effect size.
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About this digital tool
The p-value calculator approximates the p-value of a statistical test from the test statistic. Choose the test (normal Z, t with df ≥ 30 or χ² with df = 1), enter the statistic, choose whether the test is one-tailed or two-tailed and set the α level. You get the p-value and the decision: reject H₀ or fail to reject.
The p-value is the probability of getting a result at least as extreme as the observed one, if the null hypothesis is true. If p < α (usually 0.05), the null hypothesis is rejected. For z = 1.96 in a two-tailed test the p-value is about 0.05, and for z = 2.58 about 0.01. The results are normal approximations, good enough for homework and quick assessments. It is used in scientific research, medicine and A/B analysis.
How to use
- Choose the type of test (Z, t, χ², F)
- Enter the test statistic
- For a t-test: enter the degrees of freedom (df)
- Choose: one-tailed or two-tailed
- See the p-value and the statistical decision
Frequently asked questions
What does the p-value mean?
The p-value = the probability of observing this result (or a more extreme one) UNDER the assumption that the null hypothesis is true. E.g., p = 0.03 means: there is only a 3% chance we would get this result if there is no real effect.
When is the null hypothesis rejected?
When p < α (the significance level). Usually α = 0.05 (5%), but in medicine 0.01 is used, and in particle physics 0.0000003 (5σ).
What is the difference between a one-tailed and a two-tailed test?
One-tailed: you test whether the effect goes in one direction only (e.g. 'does it increase?'). Two-tailed: you test whether there is a change in either direction (e.g. 'does it change?'). A two-tailed test has a p-value twice as large.
What is the p-value for z = 1.96?
About 0.05 in a two-tailed test (about 0.025 in a one-tailed test). This is the classic threshold for statistical significance with α = 0.05.