Fisher–Snedecor F Distribution Calculator
Use this tool to compute PDF, CDF, right-tail p-value, and critical F values for hypothesis testing (ANOVA, regression F-tests, and variance comparisons).
Right-tail test uses P(F ≥ x). For most ANOVA and overall regression tests, this is the p-value you want.
What is the Fisher distribution?
The Fisher distribution (also called the F distribution or Fisher–Snedecor distribution) is a continuous probability distribution used heavily in inferential statistics. It appears whenever you compare scaled variances, especially in procedures like ANOVA and regression model tests.
It is controlled by two parameters:
- d1 = numerator degrees of freedom
- d2 = denominator degrees of freedom
Because it is asymmetric and only defined for nonnegative values, the F distribution is typically used with right-tail hypothesis tests.
When this calculator is useful
1) ANOVA tests
In one-way or multi-factor ANOVA, the test statistic follows an F distribution under the null hypothesis. You can plug in your observed F, along with the correct degrees of freedom, to get the p-value directly.
2) Overall significance in linear regression
The global F-test in regression checks whether at least one predictor has a nonzero effect. Again, the observed statistic is compared against an F distribution with model and residual degrees of freedom.
3) Variance-ratio problems
If you are comparing two normal-population variances, the ratio of sample variances can be modeled with an F distribution after selecting appropriate degrees of freedom.
How to use this fisher distribution calculator
- Enter d1 and d2 (both must be positive).
- Enter your observed F statistic.
- Click Calculate from F value to get:
- PDF at F (density)
- CDF
P(F ≤ x) - Right-tail probability
P(F ≥ x)(commonly used p-value) - Approximate two-tail probability for reference
- If needed, enter α and click Find critical F to get left-tail and right-tail critical cutoffs.
Interpreting results
The most important result for many tests is the right-tail probability:
p-value = P(F ≥ observed F)
If this p-value is below your chosen significance level (such as 0.05), you reject the null hypothesis. A small p-value means your observed F is unlikely under the null model.
Formula reference
This page computes the CDF using the regularized incomplete beta function relationship:
F_CDF(x; d1, d2) = I_{ d1x / (d1x + d2) }(d1/2, d2/2)
Critical values are found numerically by inverting the CDF via binary search, which is stable for practical statistics work.
Common mistakes to avoid
- Swapping d1 and d2 (this changes results).
- Using the left-tail probability when your hypothesis test is right-tailed.
- Entering α as 5 instead of 0.05.
- Using an F-table row/column that does not match your exact degrees of freedom.
Quick example
Suppose your ANOVA gives F = 2.5, with d1 = 5 and d2 = 10. Enter these values and click Calculate from F value. If right-tail p-value comes out below 0.05, then your factor effect is statistically significant at the 5% level.
Final note
This fisher distribution calculator is built for speed and clarity, making it a practical replacement for printed F distribution tables. It works well for coursework, reports, and quick statistical checks in real projects.