Density function of the central F distribution: In the absence of a treatment effect, the observed ratio of treatment to error mean squares follows the F distribution, described by the density function:

 

 

where p and q are the model test and error degrees of freedom respectively, and the beta function The area under the density function above F is the probability of making a Type-I error in rejecting a true null hypothesis. The critical F_[α] is the value of F when this probability = α (often at α = 0.05).

 

Doncaster, C. P. & Davey, A. J. H. (2007) Analysis of Variance and Covariance: How to Choose and Construct Models for the Life Sciences. Cambridge: Cambridge University Press.

http://southampton.likn.co/~cpd/anovas/datasets/