F-distribution P-value

Question

How do you find the p-value for f-distrubutions without using a table? I can't get a correct answer using the table and I can't figure it out.

Answer 1

I would use technology like Excel or even a calculator that has been specifically optimized for F-distribution calculations. This is a great website just in general for statistical calculations ... this one should work well for finding the P-Value from F-Ratio Calculator (ANOVA)

https://www.socscistatistics.com/pvalues/fdistribution.aspx

you input in the parameters of interest like F-ratio, DF-numerator, DF denominator, sig level and it will calculate the values you are after.

Answer 2

There is a convenient way to find a p-value using the free online technology.

Open the site https://www.wolframalpha.com

In the Search field enter: f probability

Then enter values

numerator degree of freedom:

denominator degree of freedom:

endpoint:

and click the button "Compute".

In the output you will get the p-value as "right-tail".

Answer 3

1. The F-distribution’s p-value is the area under the curve to the right of your observed F statistic.
2. To get that exactly, you’d need to compute an integral of the F-distribution’s PDF from your F value to infinity.
3. This integral doesn’t have a simple formula and usually requires numerical methods or approximations.

Without a table its not as practical but this is how it can be done. I would suggest using a calculator to approximate the integrals. Please reach out if you would like to retry using the table.