F-Distribution Calculator

F density, cumulative probability, and quantile for numerator/denominator degrees of freedom.

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About this tool

Compute the F density, cumulative probability or quantile for any pair of degrees of freedom.

How to use

1
Step 1
Choose PDF, CDF or inverse CDF.
2
Step 2
Enter df1 and df2.
3
Step 3
Enter x or a probability p and press Calculate.

How it works

F is always positive and right-skewed. The CDF at x is the share of the distribution below x, so the right-tail p-value of an F statistic is 1 − CDF. The 95th percentile is the usual α = 0.05 ANOVA cut-off.

p (right-tail) = 1 − CDF(F)      quantile(0.95) = F critical at α = 0.05

Worked example

df1 = 3, df2 = 20

Input
CDF, x = 2
Output
0.853561
Walkthrough
So an F of 2 has a right-tail p of 1 − 0.853561 = 0.1464. The 95th percentile (inverse CDF at 0.95) is 3.098391.

Limitations

  • Central F only.
  • Probabilities for inverse mode must be strictly between 0 and 1.

Questions

What is the 95th percentile of F(3, 20)?
3.0984.
What p-value does F = 2 give for (3, 20)?
About 0.146 right-tailed.
Why is F skewed?
It is a ratio of positive quantities, so it cannot go below zero.

Features

  • PDF, CDF, quantile
  • Plotted curve
  • Runs in your browser

Related resources

Guides and videos from around the web—opens on YouTube or the publisher’s site.

  • Mean, Variance and Standard Deviation

    StatQuest with Josh Starmer

    Descriptive stats behind table and test tools.

    Watch on YouTube

  • P-values and significance tests

    Khan Academy

    How critical values and p-values connect on Statistics Hub.

    Watch on YouTube

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