P-Value Calculator

The p-value is the chance of a result at least this extreme if the null hypothesis were true. It says nothing about how large or how important the effect is, and nothing about the chance that the null hypothesis is true.

A p-value is the probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one your study produced. This calculator does the last step of almost every hypothesis test: it turns a finished z, t, chi-square or F statistic into that probability. Geometrically it is a tail area under the statistic's null distribution. A right-tailed test takes everything above your statistic, a left-tailed test everything below, and a two-tailed test doubles the outer tail. For the asymmetric chi-square and F distributions the two-tailed value doubles the smaller of the two tails, capped at 1. The classic case: z = 1.96 leaves 0.9750 of the standard normal distribution below it, so two-tailed p = 2 × (1 − 0.9750) = 0.0500 — sitting exactly on the conventional five percent line and, strictly read, not below it. The caveat that matters most comes from the American Statistical Association's 2016 statement: a p-value measures surprise under the null hypothesis and nothing more. It is not the probability that the null hypothesis is true, and it says nothing about how large or how important an effect is — a tiny p can accompany a trivially small effect in a large sample. The result is also only as good as the statistic and the degrees of freedom you fed it.