Which distribution does my test use?
| Test | Statistic | df |
|---|---|---|
| z-test, large-sample proportion test | z | none |
| One-sample / paired t-test | t | n − 1 |
| Independent t-test (pooled) | t | n₁ + n₂ − 2 |
| Chi-square independence | χ² | (r − 1)(c − 1) |
| One-way ANOVA | F | k − 1, N − k |
| Pearson correlation | r → t | n − 2 |
Using a z-test
For a one-sample z-test, z = (x̄ − μ₀)/(σ/√n) when σ is known; for a proportion, z = (p̂ − p₀)/√(p₀(1 − p₀)/n). Type the z here for the p-value, or use the hypothesis testing calculator to compute z from raw summary numbers.
Common critical values
Two-tailed z: 1.645 (α = .10), 1.960 (.05), 2.576 (.01), 3.291 (.001). If |z| exceeds the value, p is below that α.
Frequently asked questions
How do I find the p-value from a test statistic?
Choose the distribution that matches your test (z, t, χ², F or r), enter the statistic and its degrees of freedom, and the calculator returns the tail area beyond it. For a two-tailed z or t test it doubles the one-tail area.
What does a p-value mean?
The probability of getting a result at least as extreme as yours if the null hypothesis were true. It is not the probability that H₀ is true, and it does not measure the size or importance of an effect (ASA statement, Wasserstein & Lazar, 2016).
Is p = .05 a magic threshold?
No. α = .05 is a convention. Report exact p-values and effect sizes with confidence intervals rather than only “significant” or “not significant”.
Why is a chi-square or F p-value always one-tailed?
Both statistics are squared quantities that grow with any departure from H₀, so only large values count as evidence. The right tail already includes departures in both directions.