**Normal approximation of power** for fixed effects is obtained from the
following algorithm, due to Winer et al. (1991, pp 136-138):

Let

.

Then

is distributed as the standardized normal distribution, with *β*
obtained from the cumulative probability at *z*. Power = 1 - *β*.

Conversely, knowing *z* = -0.842 at *β* = 0.2, it is
possible to iterate the value of *λ*, and hence *θ/σ*,
at 80% power to detect an effect for any given *p* and *q*, and hence
*F*_{[α],p,q}, and *n*.

Winer, B. J., Brown, D. R. and Michels, K. M. (1991) *
Statistical Principles in Experimental Design* 3rd edn. New York:
McGraw-Hill.

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://www.southampton.ac.uk/~cpd/anovas/datasets/