From a test statistic
P-Value Calculator for z, t and Chi-Square Tests
Turn a z, t or chi-square test statistic into a one- or two-tailed p-value, with degrees of freedom for t and chi-square and the decision at α = 0.10, 0.05 and 0.01.
p = 0.0500
Two-tailed z test, z = 1.96.
| Significance level α | Decision |
|---|---|
| 0.1 | Reject H₀ |
| 0.05 | Reject H₀ |
| 0.01 | Do not reject H₀ |
Every value is calculated in your browser from the standard normal distribution (Marsaglia’s series for Φ) and rounded to four decimals; the tables were checked cell by cell against an independent calculation. These tables give the area to the left of z. Some textbooks, including the NIST handbook, print the area from 0 to z instead, which is the left area minus 0.5 for positive z.
How the p-value is found
The p-value is the probability, if the null hypothesis is true, of a statistic at least as extreme as yours. For a right-tailed test it is the area to the right of the statistic; for a left-tailed test, the area to the left; for a two-tailed test, twice the smaller of the two. z = 1.96 gives a two-tailed p-value of 0.0500, and t = 2.228 with 10 degrees of freedom gives the same.
- Chi-square goodness-of-fit and independence tests use the right tail.
- Reject the null hypothesis when p is below your significance level α.
Common questions
Is a smaller p-value better?
A smaller p-value is stronger evidence against the null hypothesis. It does not measure how large or important an effect is.
One-tailed or two-tailed?
Use one tail only when the alternative hypothesis names a direction before you see the data (greater than or less than). Otherwise use two tails.
The studio notebook
A useful place to begin.
Clear steps, considered details, and ideas you can put to use.
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