A p-value is the probability of obtaining results at least as extreme as the observed data, assuming the null hypothesis is true. A small p-value suggests the null hypothesis may be false.

What is the significance threshold?

The most common threshold (alpha) is 0.05, meaning a 5% chance of a false positive. Some fields use 0.01 for stricter criteria. If p < alpha, the result is considered statistically significant.

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

A one-tailed test checks for an effect in one direction only (e.g., greater than). A two-tailed test checks for an effect in either direction. Use two-tailed unless you have a specific directional hypothesis.

When should I use a T-test vs Z-test?

Use a Z-test when the population standard deviation is known or the sample size is large (n > 30). Use a T-test for small samples with unknown population variance. As degrees of freedom increase, the T-distribution approaches the normal distribution.

Does a low p-value prove my hypothesis?

No. A low p-value means the data is unlikely under the null hypothesis, but it does not prove the alternative hypothesis is true. Statistical significance is not the same as practical significance.

Math

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P-Value Calculator — Statistical Significance Test

Calculate p-values for Z-tests and T-tests, one-tailed and two-tailed. Determine statistical significance at 0.05 and 0.01 levels.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The p-value calculator computes the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. It supports Z-tests (standard normal distribution) and T-tests (Student's t-distribution), for both one-tailed and two-tailed tests.

Test Type

Tail Type

Test Statistic

What is P-Value Calculator — Statistical Significance Test?

How to use it

1️⃣ Select the test type: Z-test or T-test.
2️⃣ Enter the test statistic value (Z-score or T-score).
3️⃣ Select one-tailed or two-tailed test.
4️⃣ For T-tests, enter the degrees of freedom.
5️⃣ Click Calculate to get the p-value and significance assessment.

Formula

Z-test p-value uses the standard normal CDF approximation (Abramowitz & Stegun). T-test uses a rational approximation of the incomplete beta function. Two-tailed p = 2 × one-tailed p.

💡 See it in action — a real example

Z-test, statistic = 2.0, two-tailed: p = 2 × (1 − Φ(2.0)) = 2 × 0.0228 = 0.0455. Significant at α=0.05 but not α=0.01.

❓ Common questions

What is a p-value?: A p-value is the probability of obtaining results at least as extreme as the observed data, assuming the null hypothesis is true. A small p-value suggests the null hypothesis may be false.
What is the significance threshold?: The most common threshold (alpha) is 0.05, meaning a 5% chance of a false positive. Some fields use 0.01 for stricter criteria. If p < alpha, the result is considered statistically significant.
What is the difference between one-tailed and two-tailed tests?: A one-tailed test checks for an effect in one direction only (e.g., greater than). A two-tailed test checks for an effect in either direction. Use two-tailed unless you have a specific directional hypothesis.
When should I use a T-test vs Z-test?: Use a Z-test when the population standard deviation is known or the sample size is large (n > 30). Use a T-test for small samples with unknown population variance. As degrees of freedom increase, the T-distribution approaches the normal distribution.
Does a low p-value prove my hypothesis?: No. A low p-value means the data is unlikely under the null hypothesis, but it does not prove the alternative hypothesis is true. Statistical significance is not the same as practical significance.

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