P-Value Calculator (z, t, Chi-Square, F)
Turn a z, t, chi-square or F test statistic into a p-value: left, right or two-tailed, with critical values and the decision at α = 0.10, 0.05 and 0.01.
The p-value is the probability of a statistic at least this extreme if the null hypothesis were true. It is not the probability that the null hypothesis is true.
| α | Critical value | Statistic in rejection region? |
|---|---|---|
| 0.1 | ±1.7531 | yes |
| 0.05 | ±2.1314 | no |
| 0.01 | ±2.9467 | no |
| 0.001 | ±4.0728 | no |
A p-value tells you how surprising your test statistic would be if the null hypothesis were true. Enter a z, t, chi-square or F statistic with its degrees of freedom, choose a two-tailed or one-tailed test, and the calculator returns the exact p-value, the decision at the usual significance levels and the critical values that mark the rejection region.
How to use this tool
- Choose the distribution your test statistic follows: z for large-sample or known-σ tests, t for means, χ² for counts and variances, F for ANOVA and variance ratios.
- Enter the statistic and its degrees of freedom (two df for F).
- Pick two-tailed for "different from", or right/left-tailed for a directional hypothesis.
- Read the p-value and compare it with your significance level α.
Formula
Right-tailed p = P(X ≥ x) · left-tailed p = P(X ≤ x) · two-tailed p = 2 × min(left, right)
The t, χ² and F probabilities come from the regularized incomplete beta and gamma functions: for t, P(|T| ≥ |t|) = I_{df/(df+t²)}(df/2, 1/2); for χ², P(X ≥ x) = Q(k/2, x/2); for F, P(F ≥ f) = I_{d₂/(d₂+d₁f)}(d₂/2, d₁/2). Both tails are computed directly so very small p-values keep their significant figures.
Example
A t statistic of 2.1 with 15 degrees of freedom gives a two-tailed p-value of 0.05306. That is just above 0.05, so the result is not significant at the 5% level but is significant at 10%. The two-tailed 5% critical value for 15 df is ±2.1314, and 2.1 does not reach it.
Frequently asked questions
Should I use a one-tailed or two-tailed p-value?
Use two-tailed unless you decided before seeing the data that only one direction matters. A one-tailed p-value is half the two-tailed one for z and t, so switching after the fact overstates the evidence.
Why is my chi-square test right-tailed?
Goodness-of-fit and independence tests only reject when observed counts are far from expected, which makes the statistic large. Small values are not evidence against the null, so these tests use the right tail.
What does p < 0.05 actually mean?
If the null hypothesis were true, a statistic at least this extreme would occur less than 5% of the time. It says nothing about how big or important the effect is; report an effect size and a confidence interval as well.
Sources
Last updated:
Page address with these inputs: https://kakao.mobile/tools/p-value-calculator/
Cite or embed this tool
kakaoCalc. (2026, November 9). P-Value Calculator (z, t, Chi-Square, F). https://kakao.mobile/tools/p-value-calculator/
“P-Value Calculator (z, t, Chi-Square, F).” kakaoCalc, 9 Nov. 2026, kakao.mobile/tools/p-value-calculator/.
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