Open In App

How to Find the F Critical Value in R

Improve
Improve
Like Article
Like
Save
Share
Report

When the F test is conducted we get the F statistic as an outcome. In order to determine whether the outcome of an F test is statistically significant or not, the F statistic is compared with an F critical value. If the F-statistic comes out to be greater than F critical value then the results of the test are considered statistically significant.

For finding F critical value, we need to have the following information beforehand:

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

How to find F critical value in R:

To determine the F critical value R provides us qf() function whose syntax is given below:

Syntax:

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

Parameters:

  • p: It represents the significance level to be used
  • df1: It represents the numerator degrees of freedom
  • df2: It represents the denominator degrees of freedom
  • lower.tail = TRUE: Then the probability to the left of p in the F distribution is returned.
  • lower.tail = TRUE: Then the probability to the right is returned.
  • Note that by default lower.tail is TRUE.

Return Type:

Returns the critical value from the F distribution on the basis of the significance level, numerator degrees of freedom, and denominator degrees of freedom provided.

Example:

Let us consider an example in which we want to determine the F critical value for a significance level equal to 0.01, numerator degrees of freedom equal 4, and denominator degrees of freedom = 6.    

R




# Determine the F critical value
qf(p=.01, df1=4, df2=6, lower.tail=FALSE)


Output:

 F critical value

Interpretation of output:

Hence, the F critical value for a significance level of 0.01, numerator degrees of freedom equal to 4, and denominator degrees of freedom equal to 6 comes out to be equal to 9.14830103022785.

Therefore, if a particular type of F test is conducted then we can compare the F test statistic with 9.14830103022785. If the F statistic turns out to be more than 9.14830103022785, then the results of the test are considered statistically significant.

Relation between alpha and F critical value:

Alpha and F critical values are inversely proportional. In simple words, large alpha values lead to larger critical values and small alpha values lead to smaller critical values.

Example 1:

Let’s calculate the F critical value with the passing parameters as significance level = 0.02, numerator degrees of freedom = 6, and denominator degrees of freedom = 8 in the R programming language.

R




# Determine F critical value
qf(p=.02, df1=6, df2=8, lower.tail=FALSE)


Output:

Relation between alpha and F critical value:

Example 2:

Consider another example, having exactly the same degrees of freedom that we have taken in the above example for the numerator and denominator but the significance level to be taken is equal to 0.04:

Now let’s calculate the F-critical value again:

R




# Determine F critical value
qf(p=.04, df1=6, df2=8, lower.tail=FALSE)


Output:

Relation between alpha and F critical value:

Hence, based upon the output, we can say that value of alpha is inversely proportional to the F critical value.



Last Updated : 28 Mar, 2022
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads