What Is Hypothesis Test P-Value?
A p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. A small p-value, below your chosen α, is evidence against the null hypothesis.
Pick the distribution of your statistic, enter its value and degrees of freedom, choose the tail, and the calculator returns the p-value, the critical value, the left and right areas and the reject or fail-to-reject decision, with the p-value shaded on the curve.
The sections below explain the formulas, variables, a worked t-test example and answers to common questions about tails and what a p-value does and does not mean.
How to Use the Hypothesis Test P-Value Calculator
- Pick the type of test statistic: z, t, χ² or F.
- Enter the statistic and its degrees of freedom.
- Choose one- or two-tailed and your α.
- Read the p-value, critical value and decision.
Hypothesis Test P-Value Formula
Right-tailed p-value
Left-tailed p-value
Two-tailed p-value (z, t)
Hypothesis Test P-Value Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| s | Observed test statistic | z, t, χ² or F |
| df | Degrees of freedom | not needed for z |
| α | Significance level | commonly 0.05 |
| p | p-value | tail area beyond s |
Hypothesis Test P-Value Worked Example
A two-tailed t-test gives t = 2.31 with 24 degrees of freedom. The right-tail area beyond 2.31 is about 0.0148, so p ≈ 2 × 0.0148 = 0.0297. At α = 0.05 this is significant (0.0297 < 0.05), but at α = 0.01 it would not be.
With the example values loaded in the calculator above, the steps are:
- Test statistic t = 2.31, df = 24.
- Left area = 0.98509938; right area = 0.01490062.
- Two-tailed p = 2 × the smaller tail area (for the symmetric z and t distributions).
- Compare p = 0.0298012 with α = 0.05: p < α, so reject H₀.
Result: p-value = 0.0298012; Decision at α = Reject H₀ (p < 0.05).
How to Read a p-Value
The p-value is the probability, if the null hypothesis is true, of a result at least as extreme as the one you got. A two-tailed t-test with t = 2.31 and 24 degrees of freedom has a right-tail area of 0.0149, so p ≈ 0.0298. That is below 0.05 but above 0.01.
A p-value is not the probability that the null is true, and it does not measure the size of an effect. Pick α before you see the data, and report the actual p-value as well as the decision.
Where Hypothesis Test P-Value Is Used
From a statistic
Turn a z, t, χ² or F statistic into a p-value.
Choosing tails
See the left, right and two-tailed values.
Checking software
Confirm a p-value from another program.
Decision at α
See the critical value and the decision at your chosen α.
Common Hypothesis Test P-Value Mistakes to Avoid
- Use the right tail for F and χ² tests.
- For a symmetric statistic, the two-tailed p-value is twice the smaller one-tailed value.
- A p-value just above α is not proof of no effect.
- Report p to two or three significant figures, or as p < 0.001 for very small values.
Hypothesis Test P-Value Terms and Definitions
- p-value
- The probability, assuming H₀ is true, of a statistic at least as extreme as observed.
- Critical value
- The cut-off statistic where p equals α.
Hypothesis Test P-Value FAQs
How do I find the p-value from a test statistic?
Find the area in the tail or tails beyond your statistic, using the correct distribution and degrees of freedom. The calculator does it from the statistic and its type.
What is the p-value for z = 1.96?
For a two-tailed test it is about 0.05. The one-tailed value is about 0.025.
What does p < 0.05 mean?
If the null hypothesis were true, a result this extreme would occur less than 5% of the time. By convention you then reject H₀ at the 5% level.
Why is a two-tailed p-value double a one-tailed one?
A two-tailed test counts extreme results in both directions, so the tail area is counted twice for a symmetric distribution.