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.