P-Value Calculator

About P-Values

The p-value is the probability of observing a test statistic at least as extreme as the one computed, assuming the null hypothesis H₀ is true. A small p-value (typically below 0.05) suggests the observed result is unlikely under H₀, providing evidence to reject it. A p-value does not measure the probability that H₀ is true; it only quantifies how surprising your data would be if H₀ were true.

Two-tailed tests detect deviations in either direction (is the mean different from μ₀?), while one-tailed tests check for deviation in a specific direction (is the mean greater than μ₀?). The Z-test applies when the population standard deviation is known or the sample is large (n > 30). The T-test is appropriate for small samples with unknown population standard deviation, using degrees of freedom df = n − 1.

Statistical significance (p < 0.05) does not imply practical significance — a very large sample can produce a tiny p-value for a trivially small effect. Always interpret p-values alongside effect sizes and confidence intervals. Use our Confidence Interval Calculator and Z-Score Calculator for complementary analyses.