F‑Test P‑Value Calculator
Enter your F‑test statistic along with the numerator degrees of freedom (\(d_1\)) and denominator degrees of freedom (\(d_2\)). The p‑value is computed as: $$ p = 1 – I_{\frac{d_1 F}{d_1 F + d_2}}\Bigl(\frac{d_1}{2},\frac{d_2}{2}\Bigr). $$
* Ensure \( F \ge 0 \), \( d_1 \ge 1 \), and \( d_2 \ge 1 \).
Step 1: Enter Parameters
e.g., 4.5
e.g., 3
e.g., 20
How It Works
For an F‑test, the F‑statistic follows an F‑distribution with \( d_1 \) (numerator) and \( d_2 \) (denominator) degrees of freedom.
The cumulative distribution function (CDF) of the F‑distribution can be expressed in terms of the regularized incomplete beta function: $$ F(F; d_1, d_2) = I_{\frac{d_1 F}{d_1 F + d_2}}\Bigl(\frac{d_1}{2},\frac{d_2}{2}\Bigr). $$
The p‑value is then calculated as the probability of observing an F‑statistic greater than the computed value: $$ p = 1 – F(F; d_1, d_2). $$