The P-value Calculator converts a z-score or t-score into one-tailed and two-tailed p-values for hypothesis testing.
| P-value (x < Z, left tail) | 0.9772499 |
| P-value (x > Z, right tail) | 0.0227501 |
| P-value (0 to Z, from center) | 0.4772499 |
| P-value (−Z < x < Z, between) | 0.9544999 |
| P-value (x < −Z or x > Z, two tails) | 0.0455001 |
| One-tailed p-value | 0.036694 |
| Two-tailed p-value | 0.073388 |
In a hypothesis test, the p-value is the probability of getting a result at least as extreme as the one observed if the null hypothesis were true. A small p-value suggests the data are unlikely under the null hypothesis, which is evidence against it.
A one-tailed test looks for an effect in one direction (greater than, or less than). A two-tailed test looks for any difference and doubles the tail probability. For z = 2, the right-tail p-value is 0.0227501 and the two-tailed p-value is 0.0455003.
Researchers compare p with a significance level α, often 0.05. If p < α the result is called statistically significant. This does not prove the effect is large or important, and p-values should be reported with effect sizes and confidence intervals.
Use z when the population standard deviation is known or samples are large. Use t, with n − 1 degrees of freedom, for small samples with an estimated standard deviation.
Is p the probability the null is true? No, a common misunderstanding.
What does p = 0.05 mean? A 5% chance of seeing such data if there is no real effect.
Can p be exactly 0? No, but it can be extremely small.