When you conduct an F test, you will get an F statistic as a result. To determine if the results of the F test are statistically significant, you can compare the F statistic to an **F critical value**.

If the F statistic is greater than the F critical value, then the results of the test are statistically significant.

The F critical value can be found by using an F distribution table or by using statistical software.

To find the F critical value, you need:

- A significance level (common choices are 0.01, 0.05, and 0.10)
- Numerator degrees of freedom
- Denominator degrees of freedom

Using these three values, you can determine the F critical value to be compared with the F statistic.

**How to Find the F Critical Value in R**

To find the F critical value in R, you can use the qf() function, which uses the following syntax:

**qf(p, df1, df2. lower.tail=TRUE)**

where:

**p:**The significance level to use**df1**: The numerator degrees of freedom**df2**: The denominator degrees of freedom**lower.tail:**If TRUE, the probability to the left of**p**in the F distribution is returned. If FALSE, the probability to the right is returned. Default is TRUE.

This function returns the critical value from the F distribution based on the significance level, numerator degrees of freedom, and denominator degrees of freedom provided.

For example, suppose we would like to find the F critical value for a significance level of 0.05, numerator degrees of freedom = 6, and denominator degrees of freedom = 8.

#find F critical value qf(p=.05, df1=6, df2=8, lower.tail=FALSE) [1] 3.58058

The F critical value for a significance level of 0.05, numerator degrees of freedom = 6, and denominator degrees of freedom = 8 is **3.58058**.

Thus, if we’re conducting some type of F test then we can compare the F test statistic to **3.58058**. If the F statistic is greater than 3.58058, then the results of the test are statistically significant.

Note that smaller values of alpha will lead to larger F critical values. For example, consider the F critical value for a significance level of **0.01**, numerator degrees of freedom = 6, and denominator degrees of freedom = 8.

#find F critical value qf(p=.01, df1=6, df2=8, lower.tail=FALSE) [1] 6.370681

And consider the F critical value with the exact same degrees of freedom for the numerator and denominator, but with a significance level of **0.005**:

#find F critical value qf(p=.005, df1=6, df2=8, lower.tail=FALSE) [1] 7.951992

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