Statistics & Research Tools
P-Value Calculator
Turn a z, t, chi-square or F statistic into an exact p-value. Choose a one-tailed or two-tailed test and see instantly whether the result is significant.
What a p-value means
A p-value is the probability of seeing a result at least as extreme as yours if the null hypothesis were true. A small p-value, usually below 0.05, means the data are hard to explain by chance alone. It does not give the probability that the hypothesis is true, and it says nothing about the size or importance of an effect.
Choosing the distribution
- Z: large samples or known population variance, and tests of proportions.
- t: means of small samples, regression coefficients and correlations. Enter the degrees of freedom.
- Chi-square: tests of independence and goodness of fit. These use the right tail.
- F: ANOVA and the overall test in regression. Enter numerator and denominator degrees of freedom. These use the right tail.
One-tailed or two-tailed
Use a two-tailed test when a difference in either direction matters, which is the default in most research. Use a one-tailed test only when you decided on the direction before looking at the data and a result in the other direction would be meaningless.
Worked example
A t statistic of 2.10 with 20 degrees of freedom gives a two-tailed p-value of about 0.049. That is just below 0.05, so the result is significant at the 5% level but not at the 1% level.
Frequently asked questions
What p-value counts as significant?
The conventional threshold is 0.05, but you should set your significance level before analysing the data. Some fields use 0.01 or 0.10.
Does a high p-value prove there is no effect?
No. It only shows that your data are compatible with no effect. A small sample can fail to detect a real effect.
How do I report a p-value?
Report the exact value, for example p = 0.034, unless it is below 0.001, in which case write p < 0.001. Include the test statistic and degrees of freedom.
Why do chi-square and F tests use one tail?
Both statistics can only be positive and large values signal a poor fit to the null, so the right tail holds the evidence against it.