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P-Value Calculator
Convert a z test statistic into a p-value. Enter the z-score, choose a left-tailed, right-tailed or two-tailed test and a significance level, and the calculator gives the p-value and tells you whether the result is statistically significant.
- Result
- Significant at α = 0.05 (reject the null hypothesis)
- Area to the left of z
- 0.975002
- Area to the right of z
- 0.024998
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Formula
How to use it
- Enter your z test statistic.
- Choose the type of test your alternative hypothesis calls for.
- Choose the significance level α you set before collecting the data.
- Read the p-value; if it is below α, the result is statistically significant.
Worked examples
z = 1.96 in a two-tailed test
- P-value
- 0.049996
- Result
- Significant at α = 0.05 (reject the null hypothesis)
- Area to the left of z
- 0.975002
z = 2.5 in a right-tailed test
- P-value
- 0.00621
z = −1.2 in a left-tailed test
- P-value
- 0.11507
- Result
- Not significant at α = 0.05 (fail to reject the null hypothesis)
What a p-value is
It is the probability of getting a result at least as extreme as yours if the null hypothesis were true. A small p-value means the data would be surprising under the null hypothesis. It is not the probability that the null hypothesis is true, and it says nothing about how large or important an effect is.
Critical values and choosing a tail
For a two-tailed test, p falls below 0.05 when |z| exceeds 1.96 and below 0.01 when |z| exceeds 2.576. For a one-tailed test at 0.05 the cutoff is 1.645.
Choose one tail or two from your hypothesis before looking at the data; a one-tailed p-value is half the two-tailed one, so picking afterwards overstates the evidence.
Scope and accuracy
This calculator is for z statistics — tests with a known standard deviation or a large sample. A t statistic from a small sample needs the t distribution and will give a somewhat larger p-value.
The normal curve is evaluated to about 12 significant digits, including far into the tails: z = 8 gives a two-tailed p-value of about 1.2 × 10⁻¹⁵.
Questions people ask
What is the p-value for z = 1.96?
0.0500 for a two-tailed test (0.049996 to six places) and 0.0250 for a one-tailed test.
What is the p-value for z = 2.5 in a right-tailed test?
0.0062.
What p-value is statistically significant?
By convention, below 0.05. Some fields use 0.01 or stricter. The threshold should be chosen before the data is collected.