P-Value Calculator
Calculate the p-value from a Z or t test statistic and interpret statistical significance. Free online tool for hypothesis testing.
What is a P-Value?
The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. It measures how compatible your data are with the null hypothesis.
A small p-value (typically p < 0.05) suggests the observed result is unlikely under the null hypothesis, providing evidence to reject it. A large p-value means the data are consistent with the null hypothesis.
The p-value is not the probability that the null hypothesis is true, nor the probability that your result happened by chance alone — it is conditional on the null being true.
How P-Values Are Computed
Depending on the test direction, the p-value is the tail area under the sampling distribution of the test statistic:
p = 2·P(Z ≥ |z|) (two-tailed)
p = P(Z ≤ z) (left-tailed) / p = P(Z ≥ z) (right-tailed)
How to Use This Calculator
Follow these steps:
- Enter your observed test statistic (z or t value).
- Choose the distribution and enter the degrees of freedom when using t.
- Select the test direction (two-tailed, left-tailed or right-tailed) and read the p-value and significance conclusion.
Worked Example
A two-tailed z-test produces z = 2.10. What is the p-value?
Frequently Asked Questions
Have another question? Let us know.
What does p < 0.05 mean?
It means that, if the null hypothesis were true, the probability of observing a result at least as extreme as yours would be less than 5%. This is the conventional threshold for declaring statistical significance.
How is a p-value different from a significance level?
The p-value is computed from your data and tells you the exact probability of your result under the null. The significance level (alpha, usually 0.05) is the threshold you choose in advance. Reject the null when p < alpha.
Can a p-value tell me if my hypothesis is true?
No. A p-value only quantifies evidence against the null hypothesis. It does not measure the size of an effect or the probability that your alternative hypothesis is true.
When do I use the t-distribution instead of the normal?
Use the t-distribution when the population standard deviation is unknown and estimated from the sample, especially with small samples (typically n < 30). With large samples the t and normal distributions converge.
Related Resources
- T-Test Calculator — get the t statistic from your summary statistics
- Confidence Interval Calculator — report the CI alongside the p-value
- Normal Distribution Calculator — the curve the p-value comes from
- Z-Score Table — look up tail probabilities by hand
- Inferential Statistics — hypothesis testing guide
- Research Methods — the full statistics toolkit
