p-value Calculator
Enter a test statistic, select the reference distribution and hypotheses direction, and obtain the corresponding p-value.
p-value: 0.031555
Computed using the standard normal CDF.
How to Use This Calculator
- Select whether your test statistic follows the z or t distribution.
- Enter the observed statistic (positive or negative).
- Choose the alternative hypothesis direction (one- or two-tailed).
- Review the computed p-value and compare it with your significance level to decide whether to reject the null hypothesis.
Formulas
Two-tailed z-test: p = 2 × (1 − Φ(|z|))
Right-tailed z-test: p = 1 − Φ(z); Left-tailed: p = Φ(z)
Two-tailed t-test: p = 2 × (1 − Ft,ν(|t|))
Right-tailed t-test: p = 1 − Ft,ν(t); Left-tailed: p = Ft,ν(t)
Φ denotes the standard normal CDF, and Ft,ν is the Student's t CDF with ν degrees of freedom.
Full Description
The p-value measures how extreme the observed statistic is under the null hypothesis. Smaller p-values suggest stronger evidence against the null. Use this calculator to convert test statistics into p-values for z- or t-tests.
For other distributions such as χ² or F, use specialized calculators or statistical software packages.
Frequently Asked Questions
Can a p-value exceed 1?
No. Valid p-values always fall between 0 and 1 because they represent probabilities.
Why do t-tests require degrees of freedom?
Degrees of freedom determine the exact shape of the t distribution, reflecting sample size. Larger df values approach the standard normal distribution.
Are two-tailed p-values always double the one-tailed value?
Yes, for symmetric distributions (z or t). The calculator automatically applies this relationship.
What significance level should I use?
Common choices are 0.05 or 0.01. Reject the null hypothesis when the computed p-value is less than your chosen α.