How to Find the F Critical Value in R


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 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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