P-value Calculator
Calculate the p-value from a z, t, chi-square or F test statistic. The p-value is the probability of observing data at least as extreme as yours under the null hypothesis.
How to use the P-value Calculator
- Enter your inputs into the P-value Calculator above.
- Results update instantly as you type — no submit button needed.
- Adjust any value to see how the result changes in real time.
The p-value definition
p = P(|test stat| ≥ observed | null hypothesis true)
For a two-tailed test, integrate both tails of the test statistic's null distribution. For a one-tailed test, integrate only the tail in the alternative direction.
Worked example
A z-score of 2.33 in a two-tailed test: p ≈ 0.0198 (about 2% probability of seeing such an extreme statistic if null is true). Conventionally, p < 0.05 is "statistically significant"; p < 0.01 is "highly significant."
Frequently asked questions
What does a p-value really mean?
The probability of observing your data (or more extreme) IF the null hypothesis is true. It does NOT mean the probability the null is true, nor the probability the result is due to chance.
Why is p < 0.05 the convention?
Ronald Fisher proposed 0.05 in the 1920s as a useful threshold; it has no special mathematical status. Many fields now require lower thresholds (genomics often uses 5×10⁻⁸).
What's the difference between one-tailed and two-tailed?
Two-tailed: testing whether means differ at all (in either direction). One-tailed: testing whether one is specifically greater (or less) than the other. Two-tailed is more common and conservative.