What a critical value is
A critical value is the cut-off your test statistic must pass to be significant at a chosen level. This calculator gives the exact value for any α and degrees of freedom, including combinations printed tables leave out. See critical values explained.
Common values
| Situation | Critical value |
|---|---|
| z, two-tailed, α = .05 | ±1.960 |
| z, one-tailed, α = .05 | 1.645 |
| z, two-tailed, α = .01 | ±2.576 |
| t, df = 20, two-tailed, α = .05 | ±2.086 |
| χ², df = 4, right-tailed, α = .05 | 9.488 |
| F(3, 36), right-tailed, α = .05 | 2.866 |
Which tail?
t and z tests are usually two-tailed. Chi-square tests of association and F tests in ANOVA are right-tailed, because only large values count against the null hypothesis. A two-tailed chi-square is used for a confidence interval for a variance: with df = 10 at α = .05, the values are 3.247 and 20.483.
Accuracy
Values match SciPy’s inverse distribution functions across a grid of α and df. For printed references, see the statistical tables. To go the other way, from a statistic to a p-value, use the p-value calculator.
Frequently asked questions
What is the critical value for a 95% confidence level?
For z it is 1.96. For t it depends on the degrees of freedom: 2.086 with df = 20, for example.
How do I find a critical value in Excel?
Use =T.INV.2T(alpha, df) for two-tailed t, =NORM.S.INV(1-alpha/2) for z, =CHISQ.INV.RT(alpha, df) for chi-square and =F.INV.RT(alpha, df1, df2) for F.
What is the difference between a critical value and a p-value?
A critical value is a cut-off on the statistic's scale. A p-value is a probability. Both lead to the same decision.