An F-test produces an F-statistic. To find the p-value associated with an F-statistic in Excel, you can use the following command:
=F.DIST.RT(x, degree_freedom1, degree_freedom2)
where:
- x: the value of the F-statistic
- degree_freedom1: numerator degrees of freedom
- degree_freedom2: denominator degrees of freedom
For example, here is how to find the p-value associated with an F-statistic of 5.4, with numerator degrees of freedom = 2 and denominator degrees of freedom = 9:
The p-value is 0.02878.
One of the most common uses of an F-test is for testing the overall significance of a regression model. In the following example, we show how to calculate the p-value of the F-statistic for a regression model.
Example: Calculating p-value from F-statistic
Suppose we have a dataset that shows the total number of hours studied, total prep exams taken, and final exam score received for 12 different students:
If we fit a linear regression model to this data using study_hours and prep_exams as the explanatory variables and score as the response variable, we will get the following output:
The F-statistic for the overall regression model is 5.0905. This F-statistic has 2 degrees of freedom for the numerator and 9 degrees of freedom for the denominator.
Excel automatically calculates that the p-value for this F-statistic is 0.0332:
In order to calculate this p-value ourselves, we could use the following code:
Notice that we get the same p-value as the linear regression output.