Math
P-Value Calculator
Convert a Z, t, chi-square, or F test statistic to a p-value. Pick the tail, set alpha, and get the critical value and a significance verdict.
P-value from a test statistic
Common choices: 0.05, 0.01, 0.10.
P-value
0.049996
Scientific: 0.0500
Standard normal (Z)
Critical value
1.96
α
0.05
Reject H0 at α = 0.05. The result is statistically significant.
Frequently Asked Questions about the P-Value Calculator
What is a p-value?
The p-value is the probability of seeing a test statistic at least as extreme as the one you observed, assuming the null hypothesis is true. A small p-value means your data would be surprising under the null, which is taken as evidence against it. It is not the probability that the null is true.
When should I use each distribution?
Use Z when you have a large sample and a known population standard deviation. Use t when you estimated the standard deviation from a small sample, the usual case. Use chi-square for tests of independence or goodness-of-fit on counts. Use F for ANOVA and for comparing two variances.
One-tailed or two-tailed?
Two-tailed is the default and tests for any difference. Use one-tailed only when your hypothesis was directional before you collected data. A one-tailed test halves the p-value but only counts evidence in the predicted direction.
What does the critical value tell me?
The critical value is the test statistic that corresponds exactly to your chosen alpha. If your observed statistic is more extreme than the critical value, the p-value is below alpha and the result is statistically significant.
Why does the calculator show the p-value in scientific notation?
Very small p-values like 3.45e-5 are hard to read with leading zeros and lose precision when rounded to six decimals. The scientific form keeps the order of magnitude visible so you can compare results across orders of magnitude.