You get the p-value, its comparison with alpha, and a clear explanation without needless jargon.
This calculator converts only a Z-score into a p-value using the standard normal distribution. The p-value is the probability, assuming the null hypothesis and statistical model, of observing a score at least as extreme as the one obtained. It is not the probability that the hypothesis is true. Choose the tail and alpha level before examining the result.
For Z=2.00 in a two-sided test, the p-value is approximately 0.0455. With α=0.05 set before analysis, p<α and the result crosses the statistical threshold; this does not describe the effect size or practical importance.
Add your numbers or start with sample data.
Complete the fields to see the result and interpretation here.
The p-value assumes the null hypothesis; it is not the chance that the null is true.
Choose the tail before you inspect the result.
An effect can be statistically significant yet too small to matter in practice.
For a two-sided test, p = 2 × [1 − Φ(|z|)]. One-sided tests use the selected tail of the standard normal curve.
A p-value does not show effect size, data quality, or study power.
It measures the probability of a result at least as extreme as the observed one, conditional on the null hypothesis, the model, and the other test assumptions.
It accepts an already calculated Z-score, tail selection, and alpha. It does not run t-tests, chi-square tests, ANOVA, or calculate a p-value from raw data.
Use two-sided when effects in either direction matter. Use one-sided only for a directional hypothesis chosen before seeing the data.
No. Statistical significance does not measure size, usefulness, or impact. Read the p-value with the effect estimate, confidence interval, data quality, and context.
The references support the definitions and assumptions. The formula used is shown on this page and covered by automated tests.
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