What Is F Table?
The F distribution is the distribution of a ratio of two variances and is the basis of ANOVA, regression F tests and tests of equal variances. It takes only non-negative values and has two degrees-of-freedom parameters, df₁ for the numerator and df₂ for the denominator.
Choose critical value to get the cut-off F* for a chosen α, or p-value to turn an observed F into a probability. A table shows the critical values for your degrees of freedom at α from 0.10 to 0.001, so the tool doubles as an F table.
Below are the formulas, variables, a worked ANOVA example and answers about reading an F table.
How to Use the F Table Calculator
- Choose critical value or p-value.
- Enter the numerator and denominator degrees of freedom.
- Enter α or the F statistic.
- Read the result and the table for your degrees of freedom.
F Table Formula
F as a variance ratio
ANOVA F
Mean
F Table Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| df₁ | Numerator degrees of freedom | groups − 1 in one-way ANOVA |
| df₂ | Denominator degrees of freedom | N − groups |
| F | F statistic | ratio of variances |
| α | Significance level |
F Table Worked Example
An ANOVA with 4 groups and 24 observations has df₁ = 3 and df₂ = 20. At α = 0.05 the critical value is 3.098. If the observed F is 3.5, it exceeds the cut-off, so the group means differ significantly (p ≈ 0.035).
With the example values loaded in the calculator above, the steps are:
- Right-tail critical value: F such that P(F ≥ F*) = α = 0.05, with df = (3, 20).
- F* = 3.09839.
Result: Critical value F(3, 20) at α = 0.05 = 3.09839.
How to Read an F Critical Value
The F distribution compares two variances and is used in ANOVA and regression tests. For df₁ = 3 and df₂ = 20 at α = 0.05, the critical value is 3.098. An observed F above it means the result is significant at that level.
The test is right-tailed, because large F values signal that the between-group variation is large compared with the within-group variation. The table on this page lists the right-tail critical values for your degrees of freedom.
Where F Table Is Used
ANOVA
Find the cut-off for the F statistic from a one-way ANOVA.
Regression
Check the overall F test of a regression model.
Variance comparison
Compare two sample variances with an F test.
Replacing a printed table
Get exact values for any pair of degrees of freedom.
Common F Table Mistakes to Avoid
- The numerator degrees of freedom come first. Swapping them gives a different value.
- For ANOVA, df₁ is the number of groups minus 1 and df₂ is the total sample size minus the number of groups.
- F is always positive and the test is right-tailed.
- If your F is larger than the critical value, the p-value is smaller than α.
F Table Terms and Definitions
- Numerator df
- Degrees of freedom of the variance in the top of the F ratio.
- Denominator df
- Degrees of freedom of the variance in the bottom of the ratio.
F Table FAQs
How do I read an F table?
Find the column for the numerator degrees of freedom and the row for the denominator degrees of freedom, at the table for your α. The entry is the critical value.
Why is the F test right-tailed?
F is a ratio of variances, so a large value points to large differences between the groups. Small values are consistent with equal variances.
What is the critical F for df = (3, 20) at 0.05?
It is 3.098. The calculator also gives other α values for the same degrees of freedom.
What does the F distribution describe?
It describes the ratio of two independent scaled chi-square variables, and so it describes how the ratio of two sample variances behaves when the population variances are equal.