Effect size (delta) is specified by the difference between the largest mean and the smallest mean, in units of the within-cell standard deviation ( sigma = the square root of the MSE):

largest mean - smallest mean delta = ---------------------------- sigmaThe

Effect size delta values are typically in the range of 0 - 3. In social science applications, values of delta = 0.25, 0.75, and 1.25 or greater correspond to "small", "medium", and "large" effects, according to Cohen & Cohen, Statistical Power Analysis for the Behavioral Sciences.

However, the program can also be used for ANY fixed effect in ANY crossed factorial design, by designating the levels of the effect of interest as 'A', and the levels of all other crossed factors as 'B'.

**Examples**:

- Specify b=1 for a one-way design.
- In a 4 x 3 x 2 design, there are 6 combinations of factors 2 and 3 for each level of the first factor, so specify b=6. The sample sizes calculated are for each level of Factor A, so divide the reported values by 6 to get treatment cell sizes.
- To determine the power or sample size for the BxC interaction in a 4x3x2 design, specify a=6 (the combinations of factors B and C), and b=4 (levels of factor A for each BC combination. The delta values here refer to the BC treatment means.

Michael Friendly