P-Value Calculator

Calculate p-value from z-score, t-score, or chi-square statistic. Determine statistical significance: if p < 0.05 reject the null hypothesis. Supports one-tailed and two-tailed tests.

📊 Statistics📐 p = P(Z > |z|) for two-tailed🔢 Math
Test type
Test statistic (z, t, or chi²)
Degrees of freedom (t or chi² only)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
P-Value Calculator—p = P(Z > |z|) for two-tailedprobability 0-1

Step-by-Step Examples

Example 1
Drug Trial Z-test

A drug reduces blood pressure. Z-statistic = 2.58. Is it significant at α=0.05?

  • Two-tailed p = 2 × P(Z > 2.58)
  • p ≈ 2 × 0.0049 = 0.0099
  • p = 0.0099 < 0.05: reject null hypothesis
  • Drug effect is statistically significant
✓ p = 0.0099 — significant at α=0.05
Example 2
Borderline Result

Z = 1.96 (the classic boundary value).

  • p = 2 × P(Z > 1.96) = 2 × 0.025 = 0.050
  • Exactly at the α=0.05 threshold
  • Conventional decision: borderline significant
  • Most researchers require p < 0.05 strictly
✓ p = 0.050 — exactly at significance boundary
Example 3
Not Significant

Z = 1.20 from a sample comparison.

  • p = 2 × P(Z > 1.20) = 2 × 0.1151 = 0.2302
  • p = 0.23 > 0.05: fail to reject null hypothesis
  • Difference is not statistically significant
  • Need larger sample size or different approach
✓ p = 0.23 — not significant

Real-World Applications

💊
Clinical Trials
p-values determine whether new treatments work significantly better than placebo.
🧪
Scientific Research
Every published research paper reports p-values to validate experimental findings.
📊
Quality Control
Manufacturing uses statistical tests to detect defects — p-values trigger process adjustments.
💼
Business Analytics
A/B testing for websites, ads, and products relies on p-values to confirm real improvements.

Common Mistakes to Avoid

⚠️
Confusing p-value with the probability the null is true

p-value is NOT the probability that H0 is true. It is P(data this extreme | H0 is true). A p=0.04 does not mean 4% chance the null is true.

⚠️
Treating p=0.05 as a magic cutoff

0.05 is arbitrary convention. A p=0.049 is not fundamentally different from p=0.051. Consider effect size and practical significance too.

⚠️
Using one-tailed when two-tailed is appropriate

Only use one-tailed if you had a specific directional hypothesis BEFORE seeing the data. Choosing one-tailed after seeing results inflates false positive rate.

Frequently Asked Questions

What is a p-value? ▾
The probability of observing results as extreme as yours (or more extreme) if the null hypothesis were true. Small p-value: your data is unlikely under H0, suggesting H0 may be false.
What does p < 0.05 mean? ▾
By convention, p < 0.05 means less than 5% chance of this result if H0 were true. This is the typical threshold for claiming statistical significance. Many fields now use p < 0.01 or even p < 0.005.
What is the difference between one-tailed and two-tailed tests? ▾
Two-tailed: tests if mean differs in either direction (more common). One-tailed: tests only one direction (e.g., only testing if a drug improves, not worsens). Two-tailed is more conservative and generally preferred.
Can p-value tell me if my result is practically important? ▾
No. A tiny p-value with a huge sample can come from a trivially small effect. Always report effect size (Cohen's d, r, etc.) alongside p-value for practical interpretation.
What is Type I error? ▾
Falsely rejecting a true null hypothesis. α = 0.05 means 5% chance of Type I error. If you run 20 tests and all nulls are true, expect about 1 false positive just by chance.

Related Math Calculators

📊 T-test📊 Z-score📊 Confidence Interval📊 Chi-square Test📊 Sample Size

Formula Explorer connections

Interpretation: This relationship converts, summarizes or checks numerical quantities using standard arithmetic and measurement rules. Assumption: Use consistent units, preserve enough significant digits, and round only the final result unless the method states otherwise.

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