P-Value Calculator
Enter a z-score or t-statistic to find the corresponding p-value.
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Understanding P-Values
The p-value quantifies the strength of evidence against the null hypothesis. A p-value of 0.05 means there is a 5% probability of seeing results this extreme if the null hypothesis were true.
A small p-value (typically ≤ 0.05) leads to rejecting the null hypothesis. However, p-values do not measure the probability that the hypothesis is true or false, nor do they measure effect size.
The p-value is the probability of observing a test statistic at least as extreme as the one calculated, assuming the null hypothesis is true. A small p-value (typically p < 0.05) is evidence against the null hypothesis — not proof it is false.
For a one-sample z-test, the test statistic is z = (x̄ − μ₀) / (σ/√n). Example: a sample of 40 items has mean 98.6, against a null hypothesis mean of 100. With σ=5: z = (98.6 − 100) / (5/√40) = −1.4 / 0.79 = −1.77. Two-tailed p-value ≈ 0.077, above 0.05 — insufficient evidence to reject the null at 5% significance.
Common misconceptions: a p-value is not the probability the null is true, not the probability you made an error, and not a measure of effect size. A very small p-value in a large study may correspond to a trivially small and practically meaningless effect.
Significance thresholds (0.05, 0.01, 0.001) are conventions, not bright lines. Report the actual p-value and effect size together so readers can judge practical significance, not just statistical significance.
See also: Confidence Interval Calculator · Chi-Square Calculator