P-Value Calculator
Calculate a two-tailed p-value from a z-score.
How to use the P-Value Calculator
Enter a z-score to estimate its two-tailed p-value under the standard normal distribution. Smaller p-values indicate results that are less compatible with the null hypothesis.
Formula
Two-tailed p = 2 × (1 − Φ(|z|)). Statistical significance depends on the threshold selected for your analysis.
Understanding P-Values
A p-value measures how compatible observed data are with a statistical model under a stated null hypothesis. A small p-value can indicate that the observed result would be unusual if the null hypothesis were true, but it does not measure the size or practical importance of an effect.
P-Value Example
If a two-tailed z-test produces z = 2.00, the p-value is approximately 0.0455. At a significance level of 0.05, that result would commonly be described as statistically significant, provided the assumptions of the test are appropriate.
How to Interpret the Result
Compare the calculated p-value with a significance threshold chosen before interpreting the test. Also consider sample size, effect size, study design and confidence intervals rather than relying on the p-value alone.
Frequently Asked Questions
Does p < 0.05 prove a hypothesis?
No. It indicates the data are relatively inconsistent with the null model at that threshold; it does not prove the alternative hypothesis.
Can a large sample produce a small p-value?
Yes. Very large samples can make small effects statistically detectable, which is why practical significance matters too.
Is this calculator one-tailed or two-tailed?
This tool calculates a two-tailed p-value from a z-score.
Interpreting a P-Value
A p-value is the probability, under the specified null hypothesis and statistical model, of obtaining a result at least as extreme as the observed result. It is not the probability that the null hypothesis is true and does not measure effect size. Interpretation should consider study design, assumptions, sample size and a preselected significance level.
Calculation Details and Edge Cases
A p-value is the probability, under the null hypothesis and model assumptions, of obtaining results at least as extreme as the observed result. It is not the probability that the null hypothesis is true, and statistical significance does not by itself measure effect size or practical importance.