Hypothesis Testing Calculator
Turn a test statistic into a p-value and a decision — for z, t, chi-square or F — with the critical value and a plain reading of what it means.
Every test reduces to the same act: locate your statistic on a reference distribution and measure the tail beyond it.
How the hypothesis testing calculator works
Every test reduces to the same act: locate your statistic on a reference distribution and measure the tail beyond it. That tail is the p-value — the probability of a result at least this extreme if the null hypothesis were true.
What it is not: the probability that the null is true, the probability the result was a fluke, or a measure of how big the effect is. Those confusions are so common that this page states them explicitly.
Formula: p = P(statistic at least this extreme | H₀ true)
Worked examples
| Inputs | p-value | Note |
|---|---|---|
| z = 2.1, two-tailed | 0.03572871 | p = 0.036 — significant at 5% |
| t = 2.1 on 25 df | 0.04598428 | p = 0.046 — larger than the z version |
| A statistic of zero | 1 | p = 1 |
FAQFrequently asked questions
What is a p-value?
The probability of observing a result at least this extreme if the null hypothesis were true.
What is it not?
It is not the probability the null is true, not the probability the finding is a fluke, and it says nothing about the size or importance of an effect.
Is p = 0.049 meaningfully different from p = 0.051?
No. The 0.05 threshold is a convention, and treating it as a boundary between real and unreal is the single biggest misuse of the whole framework.
What if I ran many tests?
Correct for it. Twenty independent tests at 5% give about a 64% chance of at least one false positive. Bonferroni is crude but safe; Benjamini–Hochberg is usually better.
Should I report anything else?
Always: the effect size and a confidence interval. A p-value alone answers only the least interesting question you can ask of your data.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.