F Distribution Table
Find critical F values by selecting the numerator degrees of freedom, denominator degrees of freedom and upper-tail significance level. The reference grid and worked examples explain how to read an F table correctly.
Numerator df1 = 3; denominator df2 = 20; upper-tail α = 0.05
Critical F values are rounded for display. The numerator and denominator degrees of freedom are not interchangeable.
F Distribution Critical Values Table
An F distribution is indexed by two degrees-of-freedom parameters. Its commonly used reference table shows upper-tail critical values: the value Fcrit for which the probability of a larger F statistic equals the chosen α.
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How to Read an F Table
First find the numerator degrees of freedom (df1) and denominator degrees of freedom (df2), then choose the significance level α. Locate the corresponding row and column in the table. For df1 = 3, df2 = 20 and α = 0.05, the upper-tail critical value is approximately 3.0984.
F Table for ANOVA
In a conventional one-way ANOVA, df1 is associated with the between-groups mean square and df2 with the within-groups mean square. The observed F statistic is compared with an appropriate upper-tail critical value, subject to the assumptions of the analysis.
F Table at 0.05 and 0.01
Changing α changes the critical F threshold. For df1 = 3 and df2 = 20, the upper-tail critical value is approximately 3.0984 at α = 0.05 and 4.9382 at α = 0.01.
Frequently Asked Questions
What is an F distribution table?
It is a reference grid of critical values for F distributions at specified numerator df, denominator df and tail probabilities.
Which degrees of freedom go across an F table?
Table layouts differ. Always read the axis headings: df1 is the numerator degrees of freedom and df2 is the denominator degrees of freedom.
How do I use an F table for ANOVA?
Determine the degrees of freedom for the numerator and denominator of your ANOVA F statistic, select α, and compare the observed F statistic with the corresponding critical value.
What is the F critical value at 0.05?
It depends on both degrees-of-freedom parameters. For df1 = 3 and df2 = 20, the upper-tail 0.05 critical value is about 3.0984.
Can an F statistic be negative?
The usual F statistic based on a ratio of nonnegative variance estimates is nonnegative. The F distribution has no negative support.
Why does the F table have two degrees of freedom?
The F distribution depends on both the numerator and denominator components of a variance ratio, each with its own degrees of freedom.
Sources
Reviewed: October 2026. Reference grids and lookups are calculated locally; no observations are sent to a server.