How to Calculate P Value
What is P Value?
A p-value calculator computes the probability of obtaining results at least as extreme as observed, assuming the null hypothesis is true. A small p-value (< 0.05) suggests evidence against H₀.
Formula
p-value = P(observing result this extreme | H₀ is true); Significant if p < α (usually 0.05)
- p
- P-value (probability 0-1)
- α
- Significance level (usually 0.05)
- H₀
- Null hypothesis — No effect/difference
Step-by-Step Guide
- 1p-value < α: reject H₀ (result is "statistically significant")
- 2p-value ≥ α: fail to reject H₀ (insufficient evidence)
- 3One-tailed: directional hypothesis; two-tailed: any difference
- 4p-value does NOT equal the probability that H₀ is true
Worked Examples
Input
z = 2.33, one-tailed test
Result
p = P(Z > 2.33) = 0.0099 < 0.05 — statistically significant
Frequently Asked Questions
What does p=0.03 mean?
3% probability of observing this result if null hypothesis is true. Common threshold: p<0.05 = "statistically significant".
Does p<0.05 mean 95% chance the result is real?
No. Common misunderstanding. p<0.05 means 5% chance of this result under null hypothesis. Doesn't measure probability hypothesis is true.
When should I use p<0.05 vs p<0.01?
p<0.05 standard. p<0.01 for stricter standards (medical, critical). p<0.10 exploratory research.