Free P-Value Calculator
Estimate the two-tailed p-value for a z-test using the standard normal distribution PDF-based approximation.
Approx. Two-Tailed P-Value
0.041889
Approx. Two-Tailed P-Value vs Z-Statistic (or test statistic)
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.
Example Calculation
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
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Understanding the Normal Distribution
Learn what the normal distribution is, why it matters in statistics, and how to use the bell curve for probability calculations, z-scores, and real-world data analysis.