P-value calculator
Pick the distribution of your test statistic, enter the value and the degrees of freedom, and choose the tail. The result is the probability of a statistic at least that extreme if the null hypothesis is true.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose z, t, χ² or F and type the statistic.
- Enter the degrees of freedom the test needs (none for z; two for F).
- Choose the tail that matches your alternative hypothesis, and optionally α.
How it works
The normal tail uses the complementary error function. The t, F and χ² tails use the regularised incomplete beta and gamma functions, the same code as the t-test, ANOVA and chi-square calculators. The left tail is one minus the right tail, so very small left-tail values lose digits.
Worked example
A two-sided z-test gives z = 1.96. The right tail is 0.0249979, doubled 0.0499958. With α = 0.05, p ≤ α and the null hypothesis is rejected, though only just.
Tips
- Choose the tail before you look at the data, from the alternative hypothesis.
- A small p-value says the data are unlikely under the null; it does not say how large or important the effect is.
- For raw data, use the z-test, t-test or chi-square calculators, which compute the statistic for you.
Frequently asked questions
What is a p-value?
The probability, assuming the null hypothesis is true, of getting a test statistic at least as extreme as the one you observed. It is not the probability that the null hypothesis is true.
How is the two-sided p-value computed?
For z and t, which are symmetric, it is twice the right-tail probability of the absolute value. χ² and F are not symmetric, so the tool doubles the smaller of the two tail probabilities and caps the result at 1. Many χ² and F tests use only the right tail.
Do my values match tables?
They should. For example z = 1.96 gives 0.04999 two-sided; t = 2.228 with 10 degrees of freedom gives 0.05 two-sided; χ² = 3.841 with 1 degree gives 0.05 right-tailed; F = 4.965 with 1 and 10 degrees gives 0.05 right-tailed.
Can I use non-whole degrees of freedom?
Yes. Welch's t-test gives fractional degrees of freedom, and any positive value is accepted.