How to use this calculator
- Enter or choose distribution of the statistic.
- Enter or choose test statistic.
- Enter or choose degrees of freedom.
- Enter or choose tail.
- Enter or choose significance level (α).
- The p-value updates as you type. Use Copy result or Share to keep it.
Method
Right tail p = P(X ≥ x); left tail p = P(X ≤ x); two-tailed p = 2 × min(left, right)
- X
- the test statistic’s distribution under the null hypothesis
- x
- the observed statistic
Worked example
- Under the null hypothesis the statistic follows a t-distribution with 20 degrees of freedom.
- P(T ≥ 2.5) = 0.010617.
- Two-tailed: p = 2 × 0.010617 = 0.021234, which is below α = 0.05.
A t statistic of 2.5 with 20 degrees of freedom gives a two-tailed p-value of 0.0212, significant at the 5% level.
What the result means
A small p-value means the data would be surprising if the null hypothesis were true. It is not the probability that the null hypothesis is true, and it says nothing about how large or important the effect is, so report an effect size or confidence interval alongside it.
Assumptions and limits
- The statistic really follows the chosen distribution under the null hypothesis (the test’s own assumptions hold).
- Two-tailed p for chi-square and F doubles the smaller tail; most chi-square and F tests are right-tailed.
- Does not compute the test statistic from raw data; use the matching test first.
Questions
One-tailed or two-tailed?
Use two-tailed unless you decided before seeing the data that only one direction matters. A one-tailed p is half the two-tailed p for symmetric tests, which is why switching after the fact is not legitimate.
Which tail for chi-square and F tests?
Goodness-of-fit, independence and ANOVA tests are right-tailed: large values are evidence against the null.