Enter a z-score (test statistic) to calculate the left-tail, right-tail, and two-tail p-values for hypothesis testing.
This tool calculates the p-value for a statistical hypothesis test, helping determine whether an observed result is statistically significant or could plausibly have occurred by random chance. P-values are widely used in scientific research, A/B testing, and data analysis to support or reject a null hypothesis.
The p-value represents the probability of observing a result at least as extreme as the one measured, assuming the null hypothesis (no real effect or difference) is true. A smaller p-value indicates stronger evidence against the null hypothesis. The calculation depends on the test type (z-test, t-test, chi-square, etc.), the test statistic, and the degrees of freedom where applicable.
Enter your test statistic (such as a z-score or t-score), select the test type and tail direction (one-tailed or two-tailed), and the calculator returns the corresponding p-value.
Example: A z-score of 1.96 in a two-tailed test corresponds to a p-value of approximately 0.05, the conventional threshold for statistical significance in many fields.
What does a p-value less than 0.05 mean? It conventionally means there's less than a 5% probability the observed result occurred purely by chance, commonly interpreted as statistically significant, though this threshold is a convention, not a universal rule.
What is the difference between one-tailed and two-tailed tests? A one-tailed test checks for an effect in one specific direction, while a two-tailed test checks for an effect in either direction, which generally requires a more extreme result to reach the same significance level.
Does a low p-value prove causation? No — statistical significance indicates an association is unlikely due to chance, but it does not by itself establish that one variable causes the other.
What is the null hypothesis? It's the default assumption that there is no real effect or difference between groups being compared, which the p-value helps you assess evidence against.
Why do researchers sometimes criticize relying only on p-values? Because p-values don't measure effect size or practical significance, and results near the 0.05 threshold can be misleading if treated as a strict pass/fail cutoff rather than one piece of evidence.