After my previous post about one-sided tests, some people wondered about two-sided F-tests. And then Dr R recently tweeted:
No, there is no such thing as a one-tailed p-value for an F-test.
reported F(1,40)=3.72, p=.03; correct p=.06
use t-test for one-tailed.— R-Index (@R__INDEX) April 5, 2016
I thought it would be useful to illustrate 1) why the default F-test is never ‘two-sided’ , 2) why a one-sided F-test on two means is not possible, but a one-sided t-test for the same two means is possible, and 3) why you can not halve p-values for F-tests with more than 2 groups.
If you halve a p-value from an F-test (e.g., a p = 0.06 is reported as a ‘one-sided’ p = 0.03), you don’t end up with a directional F-test with a 5% error rate. It already was a directional F-test with a 5% error rate.
The reason is that t2has no negative values. In a F-distribution, all differences are values in the same direction. It’s like when you close a book that was open: Where all pages were on both sides of the spine in the open book (the t-test) all pages are on one side of the spine in a F-test.
This is visualized in the figure below (see the R script below this post). The black curve is an F(1,100)-distribution (did you know the F-distribution was named in honor …read more
Source:: r-bloggers.com