Imagine you have an F-Distribution with 10 degrees of freedom in the numerator.

Question

Imagine you have an F-Distribution with 10 degrees of freedom in the numerator. You want to find out the area under the curve (the definite integral) to the right of 2. For example F(10, 5) = 2, p = 0.23; F(10, 25) = 2, p = .08. If you keep the F-value and numerator degrees of freedom fixed, by increasing the denominator degrees of freedom the p-value will converge to a specific value. It turns out that in this case as the number of degrees of freedom in the denominator approaches infinity, the F-distribution will approach a chi-squared distribution. In this case the limiting chi-squared distribution will have the same number of degrees of freedom of the numerator degrees of freedom for the F-distribution (so 10). However, the value you have to use to calculate the p-value is scaled. What value in the chi-squared distribution (with 10 degrees of freedom) do you have to calculate the area to the right of so that it matches F(10, infinity) = 2?

Explanation / Answer

We are given F(10,infinty)=2

We have to find value of chisquare distribution with 10 degrees of freedom

By checking the Chi Square distribution table we find

At alpha=0.995 and df=10 the value is 2.156

But we want a exact value of 2

In excel we can type the command =CHIDIST(2,10) to get our required answer

=0.99634

This is the value which exactly matches F(10,infinity)=2

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.