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.

Output:

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:

Output:

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

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