Statistical Tables & Calculators
The tables at the back of your textbook, reimagined. Pick a distribution, type your statistic (or your α), and get the exact p-value or critical value — with the tail area drawn so you can see what the number means.
🎛️ Distribution calculator
Everything updates as you type. The shaded region is the probability being reported.
How to use it
- Got a test statistic? (from software, a homework problem, or a formula) — choose its distribution, enter it, and read the exact p-value. For t and z, pick the tail your hypothesis calls for; χ² and F tests are naturally right-tailed.
- Need a critical value? Switch to the α mode. The shaded region is the rejection region: a statistic landing inside it means p < α.
- Checking a printed table? The "critical values at common α" row below the chart is the entire relevant column of a z, t, χ², or F table for your degrees of freedom.
These are exact values, not approximations. The calculator uses the same special functions (incomplete gamma and beta) that R and Python use under the hood — the numbers match pnorm, pt, pchisq, and pf to many decimal places.
Common critical values worth memorizing
| Confidence / α (two-tailed) | z critical | Where you'll meet it |
|---|---|---|
| 90% · α = .10 | 1.645 | Lenient exploratory cutoffs |
| 95% · α = .05 | 1.960 | The default in most of science |
| 99% · α = .01 | 2.576 | Stricter confirmatory tests |
| 99.9% · α = .001 | 3.291 | Very strong evidence claims |
t critical values are always a little larger than these (fatter tails), and they shrink toward the z values as degrees of freedom grow — by df ≈ 120 the difference barely matters. Try it above.
Where these distributions come from
- Normal (z) — the bell curve behind z-scores and the Central Limit Theorem. See the lesson →
- Student's t — the fat-tailed cousin used when the SD is estimated from the sample. See the lesson →
- Chi-square (χ²) — the distribution of squared deviations, used for tests on counts. See the lesson →
- F — the ratio of two variances, the engine of ANOVA and regression tests. See the lesson →
Want to drag their parameters around and watch the shapes respond? Try the Distribution Playground — and the formula sheet has every formula these tests are built from.