A p-value is the probability of observing a test statistic at least as extreme as the one computed, assuming the null hypothesis is true. A small p-value (e.g., < 0.05) suggests the result is statistically significant.

When should I use a z-test vs a t-test?

Use a z-test when the population variance is known or the sample size is large (n > 30). Use a t-test when the population variance is unknown and the sample size is small; the degrees of freedom equal n - 1 for a one-sample test.

What is the difference between one-tailed and two-tailed tests?

A two-tailed test checks for an effect in either direction (H1: μ ≠ μ0). A one-tailed test checks for an effect in one specific direction (H1: μ > μ0 or H1: μ < μ0). Two-tailed p-values are twice the one-tailed value.

How accurate are the results?

The z-test uses Abramowitz & Stegun's rational approximation (error < 7.5 × 10⁻⁸). The t-test uses an iterative incomplete-beta method accurate to at least 6 significant figures for practical degrees of freedom.

What does a p-value of 0.05 mean?

It means there is a 5% chance of obtaining a test statistic as extreme as yours if the null hypothesis were true. By convention, p < 0.05 is considered statistically significant, though this threshold is context-dependent.

P Value Calculator

Name: P Value Calculator
Availability: InStock
Author: Nham Vu

Calculate the p-value from a z-score or t-statistic for one-tailed and two-tailed hypothesis tests.

Test Parameters

Test Type

Z-Score

Enter a positive or negative value.

Hypothesis Tails

Enter a test statistic and click Calculate

P-Value

Test Statistic

Test Type

Tails

Significance Thresholds

Alpha (α)	Significant?	Confidence Level

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Summary

Calculate the p-value from a z-score or t-statistic for one-tailed and two-tailed hypothesis tests.

How it works

Choose a Z-Test (population variance known or large sample) or a T-Test.
Enter your z-score, or your t-statistic together with the degrees of freedom.
Select a one-tailed or two-tailed alternative hypothesis.
The tool computes the tail probability under the null hypothesis and reports the p-value.
Compare the p-value to your significance level (e.g. 0.05) to decide whether the result is significant.

Use cases

Determine statistical significance of a research finding.
Verify p-values from regression or ANOVA output.
Teach hypothesis testing concepts interactively.
Quick sanity-check during data analysis.
Compare one-tailed vs two-tailed test outcomes.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu