F Distribution Table (F-Table)

4 min read Joseph Mburu
Statistical Tables

Use this interactive F distribution table to find the F critical values for α = 0.10, 0.05, 0.025, 0.01, and 0.005. Select an alpha level, choose the numerator degrees of freedom, df₁, denominator degrees of freedom, df₂, and click "find critical value." The matching F critical value will be highlighted in the table.

Find an F Critical Value

The table shows upper-tail F critical values.
Usually the degrees of freedom for the numerator.
Usually the degrees of freedom for the denominator.

F Table

Upper-tail F critical values are shown.

Note: This F table shows upper-tail critical values. For many F tests and ANOVA problems, you use the upper-tail value based on the chosen alpha level, numerator df₁, and denominator df₂.

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. Sometimes, the table is also referred to as the F-critical value table because it helps you find the critical value for F-tests such as ANOVA, regression, and F-tests for comparing two variances.

How to Use This Interactive F Table

This interactive F-table will help you quickly find the correct F critical value for the most common significance levels (α = 0.10, 0.05, 0.025, 0.01, and 0.005), without manual lookup. 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 will instantly use the correct F-table, depending on the selected significance level (α), and highlight the matching value in the table.

Want to download the F tables in PDF format? Select the significance level, choose df1=120 and df2 = 120, and click the “print/save as PDF” button.

Example 1. Automatic Look Up

Find the critical value for a one-way ANOVA with df1 = 10 and df2 = 20. Use the 0.01 level of significance.

Solution

To find the F-critical value, F0.01, 10, 20, using the interactive F-table, follow these steps:

  1. Select the significance level, α = 0.01
  2. Select the numerator degrees of freedom, df1 = 10
  3. Select the denominator degrees of freedom, df2 = 20
  4. Click “Find critical value”

The table will automatically highlight the critical value as 3.368. Therefore, F0.01, 10, 20 = 3.368.

How to Read an F Distribution Table Manually

An F-table has numerator degrees of freedom (df1) as the columns across the top, and denominator degrees of freedom (df2) as the rows down the side. Each of the tables has a different significance level (α) reported at the top. Therefore, before using an F-table, always make sure it has the correct significance level, say α = 0.05, α = 0.01, α = 0.10, etc.

To find the F-critical value manually from F tables, follow these steps:

  1. Find the specific table matching your significance level (α)
  2. Move across the top row to locate your numerator degrees of freedom (df1)
  3. Move down the leftmost column to locate your denominator degrees of freedom (df2)
  4. The number where that row and column meet is your critical F-value.

Example 2. Manual Look Up

A psychology student is conducting an ANOVA test to compare reaction times across four different stimulus groups. She needs to find the threshold value to determine statistical significance. Find the critical F-value given the following experimental parameters:

  • Total number of participants, n = 24
  • Number of groups, k = 4
  • Significance level, α = 0.01

Solution

To find the correct critical value for the F-test, we need to first calculate the degrees of freedom.

By definition:

  • The numerator degrees of freedom, df1 = k-1
    • = 4 -1 = 3
  • The denominator degrees of freedom, df2 = n-k
    • = 24-4 = 20

Alternatively, you can quickly find these degrees of freedom using the degrees of freedom calculator.

Since we have all the required parameters, we can read the correct F-critical value from an F table as follows:

  1. Find an F-distribution table with α = 0.01
  2. Move across the top row to locate df1 = 3
  3. Move down the leftmost column to locate df2 = 20
  4. Locate the value where that row and column meet

The row and column meet at 4.938. Therefore, the correct F-critical value for the test: F0.01, 3, 20 = 4.938.

F-critical value example using F-table

When to Use an F Table?

The F-table is commonly used to find the critical value for test statistics that follow an F-distribution. Common situations include:

  • testing differences among group means in ANOVA
  • testing the overall significance of a regression model
  • comparing two sample variances
  • checking whether a calculated F statistic is large enough to be significant

An F table is most useful when your alpha level and degrees of freedom are listed in the table. However, if you can’t find the exact values in the table, you should use the F-critical value calculator for a more precise result.

Frequently Asked Questions

What is an F table?

An F table is a statistical table used to find F critical values based on alpha level, numerator degrees of freedom, and denominator degrees of freedom.

How do I read an F table?

Choose the alpha level first. Then find the numerator degrees of freedom across the top and the denominator degrees of freedom down the side. The value where the row and column meet is the F critical value.

What alpha levels are included in this F table?

This F table includes common significance level values you’ll come across in your coursework. These include α = 0.10, 0.05, 0.025, 0.01, and 0.005.

Is the F table left-tailed or right-tailed?

This table shows upper-tail, or right-tail, F critical values. These are the values most commonly used in ANOVA, regression F tests, and F tests comparing variances.

What should I do if my df value is not in the table?

Use the closest value required by your course. Alternatively, you can use the F critical value calculator for a more exact result.