StatReason

P-Value Calculator

Convert an already-computed test statistic into a p-value directly, choosing the null distribution it belongs to and the tail direction you care about. This calculator does not compute the statistic itself; that is each specific test's own job.

What this answers

This calculator answers "given this statistic, this reference distribution, and this alternative hypothesis, what is the exact tail probability?" It is a pure conversion, useful when you already have a statistic (from a textbook, a colleague, or another software package) and just need the matching p-value under one of the four most common reference distributions.

How it is calculated

For the standard normal and t distributions, a two-sided p-value doubles the probability of observing a statistic at least as extreme in absolute value; for the one-sided alternatives, it uses the upper or lower tail directly. Chi-square and F statistics are always nonnegative and their common test usage is one-directional (an upper-tail test), so this calculator reports the upper-tail probability for both, matching how chi-square and F tests are conventionally reported throughout this site.

Worked example

For a standard normal statistic of 1.96 with a two-sided alternative, the p-value is about .05, the exact threshold behind the common "1.96 for 95% confidence" rule of thumb. Switch to the "greater" alternative with the same statistic and the p-value is exactly half that, about .025, since a one-sided test only counts evidence in one direction.

Assumption audit

Calculated from your data: the exact tail probability for your chosen distribution, statistic, degrees of freedom (where relevant), and alternative.
Evidence to review: whether the reference distribution you selected is actually the correct one for the statistic you are converting; a t statistic run through the normal distribution option will give a subtly wrong p-value, especially with a small degrees of freedom.
You must verify: that your chosen alternative hypothesis (two-sided, greater, or less) was decided before seeing your data, not selected afterward to make a result look more significant.

What this result does not mean

A p-value is a tail probability under a stated null model, not the probability the null hypothesis is true, and not a measure of effect size or practical importance. This calculator performs no correction for multiple comparisons; converting several statistics from the same analysis without a family-wise adjustment inflates your overall false-positive rate beyond the alpha level any single p-value here suggests.

Limitations

This calculator trusts that you supply the correct degrees of freedom and the correctly computed statistic; it cannot detect a wrong statistic entered under the wrong distribution, only compute the resulting number precisely.