This appendix presents hand formulas for two-way factorial design, together with a numerical example, These hand formulas are sometimes useful in follow-up analyses of published articles. Reading an article that gives some main effect F, for example, you may wish to make a specific two-mean comparison using a confidence interval. The two means are given, but not the error term. To reconstruct the error term, compute SS A from the A means in the article using Equation 16a below. Thence get MSerror using Equation 5a (e.g., Exercises 8 and 18). Of course, the following formulas can also be used to do Anova by hand from your own raw data.
Hand Formulas for SSs for Two-Way Design.
Numerical Example for 2 × 3 Design. The above formulas follow a uniform schema, simple once understood. To illustrate, consider the following 2 × 3 design, with n = 2 subjects per cell. Bold face numbers are marginal means.
The first step is to get the SSs. From Equation 16m,