F Distribution Table (F-Table)

What Is an F Table?

An F table, also called an F distribution table, is a statistical reference table used to find critical values from the F distribution.

It is also called an F critical value table because the values in the table act as cutoff points when performing F-tests such as ANOVA, overall regression significance tests, and tests involving variances.

To find an F critical value from the table, you need:

• the significance level, α
• the numerator degrees of freedom, df₁
• the denominator degrees of freedom, df₂

The F tables on this page give upper-tail critical values. This is appropriate for common F-tests such as ANOVA and the overall F-test in regression, where large F-statistics provide evidence against the null hypothesis.

For these right-tailed tests, the decision rule is to reject the null hypothesis (H₀) if the F-statistic is greater than the F critical value and conclude that the result is statistically significant.

How to Use This Interactive F Table

The interactive F table above lets you find an F critical value without searching through a large printed table manually. It includes the commonly used significance levels α = 0.10, 0.05, 0.025, 0.01, and 0.005.

To use the table:

1. Select the significance level, α.
2. Select the numerator degrees of freedom, df₁.
3. Select the denominator degrees of freedom, df₂.
4. Click Find Critical Value.

The table automatically uses the selected significance level and highlights the F critical value corresponding to df₁ and df₂.

Example 1: Find an F Critical Value Using the Interactive Table

An ANOVA test has the following values:

• Significance level, α = 0.01
• Numerator degrees of freedom, df₁ = 2
• Denominator degrees of freedom, df₂ = 12

Find the F critical value.

Solution

Using the interactive F table:

1. Select α = 0.01.
2. Select df₁ = 2
3. Select df₂ = 12.
4. Click Find Critical Value.

The table highlights: F critical = 6.927, as shown below. Therefore, F_0.01, 2, 12 = 6.927.

If the calculated F-statistic is greater than 3.368, reject the null hypothesis and conclude that the result is statistically significant at the 0.01 significance level.

Why the F Table Uses the Right Tail

The F distribution is not symmetric like the normal distribution. It starts at zero and is typically skewed to the right.

For common F-tests such as ANOVA, large F-statistics provide evidence against the null hypothesis. Therefore, the rejection region is placed in the right tail of the F distribution.

The F critical value marks the point where the right-tail rejection region begins. The area to the right of this critical value is equal to the significance level, α.

For a right-tailed F-test:

• F-statistic > F critical → Reject H₀
• F-statistic ≤ F critical → Fail to reject H₀

If the F-statistic is greater than the critical value, it falls in the rejection region, and the result is statistically significant.

Note: Some procedures involving ratios of variances can be two-tailed. The tables on this page provide upper-tail F critical values. Always follow the decision rule specified for the particular test you are performing.

F Distribution Tables by Significance Level

Each F distribution table corresponds to a specific significance level. Before looking up a critical value, make sure you are using the table that matches the α given in your problem.

In each table:

• df₁, the numerator degrees of freedom, appears across the top.
• df₂, the denominator degrees of freedom, appears down the left side.
• The value where the df₁ column and df₂ row meet is the F critical value.

F Table 0.10

The F table 0.10 gives upper-tail F critical values for a significance level of α = 0.10. Use this table when your problem specifies a 10% significance level. Locate df₁ across the top and df₂ down the left side, then read the critical value where the two meet.

F Table 0.05

The F table 0.05 gives upper-tail F critical values for α = 0.05. This is one of the most commonly used F tables because many hypothesis tests use a 5% significance level. For instance, for an ANOVA performed at α = 0.05, use this table together with the given df₁ and df₂ to find the cutoff for statistical significance.

F Table 0.025

The F table 0.025 gives upper-tail F critical values for α = 0.025. Use this table whenever your problem specifies an upper-tail probability of 0.025. This significance level can also appear in procedures where an overall α = 0.05 is divided between two tails.

F Table 0.01

The F table 0.01 gives upper-tail F critical values for a significance level of α = 0.01. Use this table when you want to perform an F-test at the 1% significance level. For the same df₁ and df₂, an F critical value for α = 0.01 will generally be larger than the corresponding critical value for α = 0.05 because a smaller area is placed in the right tail.

F Table 0.005

The F table 0.005 gives upper-tail F critical values for α = 0.005. Use this table whenever your problem specifies an upper-tail significance level of 0.005. Because the rejection region contains only 0.5% of the distribution, the corresponding critical values are generally larger than those for more common alpha levels such as 0.05.

How to Read an F Distribution Table Manually

An F table has numerator degrees of freedom, df₁, across the top and denominator degrees of freedom, df₂, down the left side.

You also need to make sure you are using the table for the correct significance level.

To find an F critical value manually:

1. Choose the F table that matches the significance level, α.
2. Find the numerator degrees of freedom, df₁, across the top.
3. Find the denominator degrees of freedom, df₂, down the left side.
4. Read the value where the df₁ column and df₂ row meet.

If you have not yet calculated the degrees of freedom for your test, you can use the degrees of freedom calculator first.

Example 2: Find an F Critical Value Manually

A statistics exam gives the following information for an F-test:

• Significance level, α = 0.05
• Numerator degrees of freedom, df₁ = 3
• Denominator degrees of freedom, df₂ = 16

Using an F table, find the critical F-value.

Solution

Since α = 0.05, we should use the F table for α = 0.05.

Then:

1. Move across the top of the table to df₁ = 3.
2. Move down the left side to df₂ = 16.
3. Find the value where the df₁ = 3 column and df₂ = 16 row meet.

The row and column meet at: 3.239, as shown below. Therefore, F_0.05, 3, 16 = 3.239.

If the calculated F-statistic is greater than 3.239, reject the null hypothesis and conclude that the result is statistically significant at α = 0.05.

When to Use an F Table

Use an F table when a statistical test produces a test statistic that follows an F distribution, and you need to determine the corresponding critical value.

Common examples include:

• ANOVA tests for differences among group means
• overall F-tests for regression models
• tests involving ratios of variances
• textbook or exam problems that specifically ask you to use an F table

For common right-tailed F-tests, you compare the calculated F-statistic with the critical value from the appropriate table.

F Table or F Critical Value Calculator?

An F table is useful when you are learning how critical values are found, completing an exam or homework problem that specifically requires a statistical table, or checking a critical value manually.

However, traditional F tables only contain selected significance levels and degrees of freedom.

If the exact significance level or degrees of freedom you need are not shown in the table, use the F critical value calculator. It calculates the F critical value directly without requiring you to choose the nearest value from a printed table.

The interactive F table above gives you both options. You can see how an F distribution table is organized and still find the required critical value automatically.

Frequently Asked Questions