Lachenbruch (1988) proposed a simple method based on the use of orthogonal contrasts to determine the sample size or power for testing main effects and interactions, and uses the normal distribution instead of the non-central F distribution. This method can be used for factorial designs of various size. The example illustrated in this paper considers a 2 x 2 factorial design. This paper will determine both sample size and power of a particular study design with anticipated (assumed) means for each cell of the 2 x 2 factorial design. Lachenbruch’s method will be compared to nQuery Advisor 6.0 (2005) and UnifyPow, a macro for the SAS System (O'Brien, 1998), O'Brien, RG and Muller, KE (1993).
McCarthy, William F., "Lachenbruch’s Method for Determining the Sample Size Required for Testing Interactions: How It Compares to nQuery Advisor and O’Brien’s SAS UnifyPow." (July 2007). COBRA Preprint Series. Working Paper 27.