How to use
- Choose the distribution — Z, t, chi-square or F.
- Enter the test statistic and degrees of freedom and choose two-tailed, left or right.
- Read the p-value; enter α below to get the critical value.
Options explained
- Method
- t and F use the regularised incomplete beta function, chi-square and normal the regularised incomplete gamma function, matching R's pt, pchisq and pf.
- Tails
- The two-tailed p-value is twice the smaller tail. Chi-square and F tests are usually right-tailed.
Worked example and critical values
For t = 2.31 with 18 degrees of freedom and Two-tailed selected, the p-value is 0.0330. That is below α = 0.05 (Significant) but not below α = 0.01 (Not significant). The critical values at α = 0.05 for 18 degrees of freedom are −2.1009 and 2.1009, and 2.31 lies beyond them, which is the same verdict.
Two-tailed critical values for Z and t (the value the statistic must exceed in absolute size):
| α | Z | t, df = 10 | t, df = 30 | t, df = 120 |
|---|---|---|---|---|
| 0.10 | 1.6449 | 1.8125 | 1.6973 | 1.6577 |
| 0.05 | 1.9600 | 2.2281 | 2.0423 | 1.9799 |
| 0.01 | 2.5758 | 3.1693 | 2.7500 | 2.6174 |
Right-tailed critical values for chi-square:
| df | α = 0.10 | α = 0.05 | α = 0.01 |
|---|---|---|---|
| 1 | 2.7055 | 3.8415 | 6.6349 |
| 2 | 4.6052 | 5.9915 | 9.2103 |
| 5 | 9.2364 | 11.0705 | 15.0863 |
| 10 | 15.9872 | 18.3070 | 23.2093 |
As the degrees of freedom grow, the t values shrink toward the Z values.
Frequently asked questions
Does p < 0.05 mean my hypothesis is true?
No. It is the probability of a result at least this extreme if the null hypothesis were true. Consider effect size and study design too.
Can degrees of freedom be decimals?
Yes — Welch's t-test often gives non-integer degrees of freedom.
Why does it differ slightly from my table?
Printed tables list few values and are rounded; this computes the exact value.
Privacy
This tool runs entirely in your browser. Your files and text are processed on your device and are never uploaded to our servers.