P-Value Calculator
Calculate a p-value from a test statistic using normal (z), Student's t, or chi-square distributions.
What is a p-value?
A p-value is the probability of observing a result at least as extreme as your sample result, assuming the null hypothesis is true. In plain language, it helps you judge whether your observed effect looks like random noise or evidence of a real difference.
Smaller p-values suggest stronger evidence against the null hypothesis. A common threshold is 0.05, but the right cutoff depends on your field, design, and consequences of errors.
How to use this online p-value calculator
- Select a distribution: z, t, or chi-square.
- Enter your test statistic.
- Enter degrees of freedom if using t or chi-square.
- Choose left-tailed, right-tailed, or two-tailed.
- Set your significance level (alpha), then click Calculate p-value.
The tool returns the p-value and a quick significance interpretation relative to your chosen alpha.
When to use each test
Z test (normal distribution)
Use this when your test statistic follows a standard normal distribution (often with large samples or known population variance).
T test (Student's t)
Use this when estimating population variability from sample data, especially with smaller sample sizes. Degrees of freedom are required because the t distribution shape changes with df.
Chi-square test
Use chi-square for variance tests, goodness-of-fit, and contingency-table analyses. The chi-square distribution is not symmetric, which affects one-tailed versus two-tailed interpretation.
How to interpret the result correctly
- p ≤ α: Reject the null hypothesis (statistically significant).
- p > α: Fail to reject the null hypothesis (not statistically significant).
A p-value does not measure effect size, practical importance, or the probability that the null hypothesis is true. Always pair p-values with confidence intervals and domain context.
Common mistakes with p-values
- Interpreting p as the probability your hypothesis is correct.
- Ignoring whether the test should be one-tailed or two-tailed.
- Running many tests without adjustment for multiple comparisons.
- Using p-value alone to claim practical significance.
Quick example
Suppose your t statistic is 2.4 with 18 degrees of freedom, and you run a two-tailed test. Enter those values, choose T Test and Two-tailed, then calculate. If the p-value is below 0.05, the result is statistically significant at the 5% level.
Frequently asked questions
Is a smaller p-value always better?
Not necessarily. Smaller p-values indicate stronger evidence against the null, but study quality, assumptions, measurement validity, and effect size still matter.
Can I use this for hypothesis testing homework?
Yes. This calculator is useful for checking manual work and understanding tail choices. For formal reports, also document your test assumptions and sample details.
What if my p-value is exactly 0.0000?
In practice, it means the p-value is extremely small and rounds to zero at displayed precision. Report it as p < 0.0001 (or your chosen reporting standard).