What Is P Value Two Tailed Test?
A two-tailed p-value is the probability of getting a result at least as extreme as yours in either direction, if the null hypothesis is true. For a symmetric distribution it is exactly double the area in one tail beyond the absolute value of your statistic.
Choose z or t, enter the statistic and, for t, the degrees of freedom. The calculator returns the two-tailed p-value, the one-tailed p-values, the critical values for your alpha, and a clear reject or fail to reject decision, with both tails shaded on the curve.
Use a two-tailed test when a difference in either direction would matter. Switching to a one-tailed test after seeing the data is not valid, so decide the direction before you collect results.
How to Use the P Value Two Tailed Test Calculator
- Choose z or t, and enter df for t.
- Enter the test statistic and alpha.
- Read the two-tailed p-value and the decision.
P Value Two Tailed Test Formula
Two-tailed p-value
z critical value
P Value Two Tailed Test Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| z or t | The test statistic | |
| df | Degrees of freedom | t tests only |
| α | Significance level | Commonly 0.05 |
| p | Two-tailed p-value | 2 × one-tail area |
P Value Two Tailed Test Worked Example
With the example values loaded in the calculator above, the steps are:
- Statistic z = 2.15.
- One tail: P(z > 2.15) = 0.015778.
- A two-tailed test counts both tails, so p = 2 × 0.015778 = 0.031555.
- Critical values at α = 0.05 are ±1.96, and |z| = 2.15 is beyond them.
- p ≤ α, so reject H₀.
Result: Two-tailed p-value = 0.031555; Decision at α = 0.05 = Reject H₀.
Worked example: z = 2.15
The area above 2.15 is 0.01578. Doubling gives p = 0.03156. At α = 0.05 the critical values are ±1.96, and 2.15 lies beyond 1.96, so you reject H₀.
Two-tailed versus one-tailed
A one-tailed test puts all of alpha in one tail, so the same statistic can be significant one-tailed but not two-tailed. Switching to one tail after seeing the data is not valid.
Where P Value Two Tailed Test Is Used
Finishing a hypothesis test
Convert your computed statistic to a p-value.
Checking software output
Confirm a two-tailed p-value from a z or t statistic.
Exam practice
Find p-values and critical values without tables.
Common P Value Two Tailed Test Mistakes to Avoid
- The two-tailed p-value for a symmetric distribution is always twice the smaller one-tailed value.
- Report the exact p-value rather than only “p < 0.05”.
P Value Two Tailed Test Terms and Definitions
- Two-tailed test
- A test where extreme values in either direction count as evidence against the null.
P Value Two Tailed Test FAQs
How do you find a two-tailed p-value?
Find the area in one tail beyond the absolute value of the statistic and double it.
What is the two-tailed p-value for z = 1.96?
About 0.05, which is why ±1.96 are the 5% critical values.
When should I use a two-tailed test?
When you care about a difference in either direction, which is the usual default.
Is the two-tailed p-value always bigger than the one-tailed?
Yes, for a statistic in the direction of the alternative it is exactly double.
What is the difference between z and t?
Use t when the standard deviation is estimated from the sample. It has heavier tails, so its p-values are larger.
What does p = 0.03 mean?
If the null hypothesis were true, a result this extreme would occur about 3% of the time.