P-Value Calculator
Compute a p-value for a z-test or t-test.
How the p-value works
The p-value is the probability of observing a test statistic at least as extreme as the one you obtained, assuming the null hypothesis is true. It is not the probability that the null hypothesis is correct.
This calculator supports two defensible tests: the z-test (standard normal) and the t-test (Student's t with degrees of freedom). For a z-test you can enter the z statistic directly, or compute z from a one-proportion test.
Compare the p-value to your significance level (α, commonly 0.05). If p < α the result is statistically significant. Statistical significance is not the same as practical importance, and a significant result does not prove a real-world effect.
The formulas
z = (p̂ − p₀) ÷ √(p₀(1−p₀) ÷ n) · two-tailed p = 2·P(|Z| ≥ |z|)
For a one-proportion z-test, z compares the observed proportion to a hypothesized value. The p-value is then read from the normal or t distribution according to the tails you select.
Worked example
A z-test at the 5% level
If your computed z is 1.96, the two-tailed p-value is 0.05 — exactly at the conventional 5% significance level. A z of 2.58 gives p ≈ 0.01.
Frequently asked questions
What is the difference between one-tailed and two-tailed?
A two-tailed test checks for a difference in either direction; a one-tailed test checks only for an increase (upper) or only for a decrease (lower). Two-tailed is the common default.
What does statistical significance mean?
It means the observed result is unlikely under the null hypothesis at your chosen level. It does not mean the effect is large, important, or causal — that is practical significance, judged separately.
Can I always get a p-value from any statistic?
No. A p-value is only meaningful for a defined test with stated assumptions. This calculator supports the normal and t distributions; using the wrong distribution for your test gives a misleading result.
Related research methods
- Hypothesis Testing
When to use this tool
Use this to convert a computed test statistic into a p-value when you already know the distribution it follows.
Assumptions
- The test statistic follows the assumed distribution under the null hypothesis.
- The underlying test's assumptions are satisfied.
Limitations
- A p-value is not the probability that the null hypothesis is true.
- p-values are sensitive to sample size and do not convey effect size.
How to interpret the result
The p-value is the probability of observing a statistic at least as extreme as yours if the null hypothesis were true.
How to report the result
Report the p-value with the test statistic and degrees of freedom, and interpret it in the context of a pre-specified α.
Next steps in your analysis
Related tools
Related guides
- How to Choose the Right Statistical TestA practical framework for picking the right statistical test: start from your research question, data type and study design, then check the assumptions.
- Understanding P-Values and Statistical SignificanceWhat a p-value actually means, what it does not mean, the role of the significance level, and why the field is moving away from the 0.05 bright line.
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