P-Value Calculator Formula & How It Works
p-value (two-tailed) = 2 × P(Z > |z|) = 2 × (1 − Φ(|z|))
- One-tailed: p = P(Z > z) or P(Z < z)
- Two-tailed: p = 2 × P(Z > |z|)
- α = significance level (0.05 most common)
- Reject H₀ if p < α
The p-value is the probability of observing a test statistic as extreme as (or more extreme than) the one computed, assuming the null hypothesis is true. Small p-value (< 0.05) → the result is unlikely by chance → reject the null hypothesis. Large p-value → result is consistent with the null → fail to reject it. P-value ≠ probability the null hypothesis is true.