P-Value Calculator Formula
Understand the math behind the p-value calculator. Each variable explained with a worked example.
Formulas Used
Approx. Two-Tailed P-Value
approx_two_tail = 2 * phi / abs_zPDF at z
pdf_value = phiSignificant at 0.05?
significant_05 = (abs_z > 1.96) * 1Significant at 0.01?
significant_01 = (abs_z > 2.576) * 1Variables
| Variable | Description | Default |
|---|---|---|
z | Z-Statistic (or test statistic) | 2.1 |
abs_z | Derived value= abs(z) | calculated |
phi | Derived value= (1 / sqrt(2 * pi)) * pow(e, -0.5 * pow(z, 2)) | calculated |
How It Works
How to Interpret P-Values
Concept
The p-value is the probability of observing a test statistic as extreme or more extreme than the computed value, assuming the null hypothesis is true. A small p-value (typically < 0.05) provides evidence against the null hypothesis.
This calculator provides an approximation for the two-tailed p-value using the normal PDF. For exact values, consult a z-table or statistical software.
Worked Example
A z-test yields z = 2.1. Is this significant at the 5% level?
- 01|z| = 2.1
- 02PDF at z=2.1: phi(2.1) = 0.04398
- 03Approximate two-tailed p ≈ 2 * 0.04398 / 2.1 ≈ 0.0419
- 04Since 0.0419 < 0.05, the result is statistically significant at the 5% level
- 05Since 0.0419 > 0.01, it is NOT significant at the 1% level
Frequently Asked Questions
What does a p-value of 0.05 mean?
If the null hypothesis is true, there is a 5% chance of getting a result this extreme or more extreme by random sampling. It does not mean there is a 5% chance the null is true.
Is a smaller p-value always better?
A smaller p-value provides stronger evidence against the null, but statistical significance does not imply practical significance. Always consider effect size alongside the p-value.
What is the difference between one-tailed and two-tailed p-values?
A two-tailed p-value tests for any difference (positive or negative) and is double the one-tailed value. One-tailed tests have more power but assume you know the direction of the effect in advance.
Learn More
Guide
Hypothesis Testing Guide
Learn how hypothesis testing works step by step. Covers null and alternative hypotheses, test statistics, p-values, significance levels, and common pitfalls to avoid.
Ready to run the numbers?
Open P-Value Calculator