P-Value Calculator
Calculate p-values from test statistics for z-tests, t-tests, and chi-square tests. Determine statistical significance.
P-Value Result
P-Value
0.0124
Significant!
Test Configuration
Test Statistic
Result
P-Value
0.0124
p = 0.0124 ≤ α = 0.05 → Reject H₀
Test Statistic
2.5000
P-Value
0.012419
Alpha (α)
0.05
Interpretation
Strong evidence against H₀
Distribution Visualization
P-Value Interpretation Guide
Critical Values Reference
| α | Two-tailed z | One-tailed z | Two-tailed t (df=30) |
|---|---|---|---|
| 0.10 | ±1.645 | 1.282 | ±1.697 |
| 0.05 | ±1.960 | 1.645 | ±2.042 |
| 0.01 | ±2.576 | 2.326 | ±2.750 |
| 0.001 | ±3.291 | 3.090 | ±3.646 |
?How Do You Calculate a P-Value?
A p-value is the probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true. If p < 0.05 (common threshold), results are statistically significant - unlikely due to chance. P-value does NOT indicate effect size or practical importance, only statistical significance.
What is a P-Value?
The p-value is the probability of obtaining test results at least as extreme as the observed results, assuming that the null hypothesis is true. It quantifies the strength of evidence against the null hypothesis in statistical hypothesis testing. A small p-value suggests the observed data is unlikely under the null hypothesis.
Key Facts About P-Values
- P-value: probability of results as extreme as observed if null is true
- Common significance level (alpha): 0.05 (5%)
- p < alpha: reject null hypothesis (statistically significant)
- p >= alpha: fail to reject null hypothesis
- Smaller p-value = stronger evidence against null hypothesis
- P-value does NOT measure effect size or practical importance
- One-tailed vs two-tailed tests affect p-value
- Multiple testing requires p-value correction (Bonferroni, etc.)
Quick Answer
A p-value is the probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true. If p < 0.05 (common threshold), results are statistically significant - unlikely due to chance. P-value does NOT indicate effect size or practical importance, only statistical significance.
Frequently Asked Questions
A p-value is the probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true. It measures evidence against the null hypothesis. Lower p-values = stronger evidence against H₀.
A result is statistically significant when p-value ≤ α (significance level, usually 0.05). This means we reject the null hypothesis. Significance indicates the effect is unlikely due to chance alone, but doesn't measure importance or size of effect.
Use two-tailed when you're testing for any difference (H₁: μ ≠ μ₀). Use one-tailed when you have a specific directional hypothesis (H₁: μ > μ₀ or μ < μ₀). Two-tailed is more conservative and generally preferred.
Z-test assumes known population standard deviation and normal distribution (large samples, n>30). T-test is used when σ is unknown (estimated from sample) or small samples. T-test accounts for extra uncertainty in small samples.
Failing to reject H₀ means there's insufficient evidence against it, NOT that H₀ is true. It's like a "not guilty" verdict - we can't prove guilt (reject H₀), but that doesn't prove innocence (accept H₀).
Last updated: 2025-01-15
P-Value Result
P-Value
0.0124
Significant!