P-value Calculator
Enter a z-score to get every p-value a z-table provides: left tail P(Z < z), right tail P(Z > z), the area from the center, the area between ±z and the two-tailed p-value — with a significance verdict at α = 0.05.
TheCalculators — P-value Calculator
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Two-tailed p-value
0.0455
z = 2 · significant at α = 0.05 — reject H₀
- Z-score
- 2
- P(x < Z) — left tail
- 0.97725
- P(x > Z) — right tail
- 0.02275
- P(0 to Z) — from center
- 0.47725
- P(−Z < x < Z) — between
- 0.9545
- P(x < −Z or x > Z) — two tails
- 0.0455
- Verdict at α = 0.05
- Significant — reject H₀
- Verdict at α = 0.01
- Not significant
How the p-values were derived
- 1Left tail from the normal CDFP(Z < 2) = Φ(2) = 0.97725
- 2Right tailP(Z > 2) = 1 − Φ(2) = 0.02275
- 3Area between ±ZP(−Z < x < Z) = 2Φ(|z|) − 1 = 0.9545
- 4Two-tailed p-valuep = 2 × (1 − Φ(|z|)) = 2 × 0.02275 = 0.0455
Assumes a standard normal distribution (z-test). p ≤ 0.05 is the conventional threshold for rejecting the null hypothesis — smaller p means stronger evidence against H₀.
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Formula
p(left) = Φ(z) · p(two-tailed) = 2(1 − Φ(|z|)) · Φ = standard normal CDF
Pro tips
- • Use the two-tailed p unless your alternative hypothesis is explicitly one-directional.
- • |z| ≥ 1.96 ⟺ two-tailed p ≤ 0.05.
- • p is the probability of data this extreme assuming H₀ — not the probability H₀ is true.
FAQ
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