F-table

These F-tables provide the critical values for right-tail F-tests. Your F-test results are statistically significant when its test statistic is greater than this value.

F-distributions require both a numerator and denominator degrees of freedom (DF) to define its shape. For example, F_(3,2) indicates that the F-distribution has 3 numerator and 2 denominator degrees of freedom.

Choose the F-table for your significance level. These three tables cover the most common significance levels of 0.10, 0.05, and 0.01. Columns specify the numerator degrees of freedom (DF1), while rows set the denominator’s (DF2).

Learn how to use this F-table using the information, examples, and illustrations below the table.

Related post: What are Critical Values?

F-table of Critical Values for Significance Level = 0.10

F-table of Critical Values for Significance Level = 0.05

F-table of Critical Values for Significance Level = 0.01

How to Use the F-Table

Use the F-table to find the critical value for your F-test. You’ll need to know the significance level, the numerator degrees of freedom, and the denominator DF.

In the F-table, its components represent the following:

• Each table represents a different significance level (α).
• Column headings indicate the numerator degrees of freedom (DF1).
• Row headings define the denominator degrees of freedom (DF2).
• Cells within the table represent the critical F-value for a right-tailed test.

Calculating the degrees of freedom depends on the type of F-test you’re performing. Learn about the F-test in ANOVA.

Start by finding the table that corresponds to your significance level.

Then, find the intersection of the column and rows that corresponds to your numerator and denominator DF. The F-table cell at that intersection indicates the critical values for your test. When the F-test statistic is greater than this value, your results are statistically significant.

Let’s walk through an example! I’ll illustrate the answer with a probability distribution plot. It helps link the plain-looking F distribution table to something more intuitive!

Learn more about test statistics, significance levels, and degrees of freedom in hypothesis tests.

Tables for other statistics include the z-table, t distribution table, and chi-square table.

Example of Finding the Critical F-value

Suppose you use a significance level of 0.05, and your F-test has 3 numerator and 30 denominator degrees of freedom—F_{(3, 30)}.

Your first step is to locate the F-table for α = 0.05. Then find the column for 3 numerator DF and the row for 30 denominator DF. The intersection of that row and column contains the critical F-value, as shown below.

The F-table indicates that the critical value is 2.92. If the F-test statistic is greater than or equal to 2.92, our results are statistically significant. The probability distribution plot below displays this graphically.

The shaded area is the probability of F-values falling within the rejection region of the F-distribution when the null hypothesis is true. The probability for this region equals the significance level, which is 0.05 for this example.

The F-distribution is the sampling distribution for the F-test’s test statistic. Learn more about sampling distributions.