📉 P-Value Calculator
Find one-sided and two-sided p-values from common test statistics (Z, t, χ², F) and see the decision vs α in real time.
The alternative defines how we measure “more extreme”.
This determines which CDF is used.
Example: Z = 1.96, t = 2.1, χ² = 5.4, F = 3.2
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🧮 P-value
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Pick inputs to compute the p-value.
✅ Decision vs α
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We’ll compare p with your α threshold.
📐 Step-by-step derivation
Waiting for inputs…
🔎 Reference table & sources
| Distribution | Parameters | Left-tail p | Right-tail p | Two-tail p |
|---|---|---|---|---|
| Normal (Z) | — | Φ(x) | 1 − Φ(x) | 2·min{Φ(x), 1−Φ(x)} (≡ 2·Φ(−|x|)) |
| t-Student | ν | F_t(x;ν) | 1 − F_t(x;ν) | 2·min{F_t(x;ν), 1−F_t(x;ν)} |
| Chi-square (χ²) | k | F_χ²(x;k) | 1 − F_χ²(x;k) | 2·min{F_χ²(x;k), 1−F_χ²(x;k)} |
| Snedecor’s F | k₁, k₂ | F_F(x;k₁,k₂) | 1 − F_F(x;k₁,k₂) | 2·min{F_F(x), 1−F_F(x)} |
Source: L. Wasserman, All of Statistics, Springer, 2003; standard CDF definitions. Tail rules match common practice.