Quasi F-ratio: For some mixed and random models there is no exact F-ratio denominator for certain tests. In such cases it may be possible to add and subtract mean squares to construct an error mean square with the appropriate estimated components of variation. This error mean square is then used to obtain a quasi F-ratio.
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.