Sample size required for mixed design ANOVA to achieve adequate statistical power

Question

Context

I ran an experiment with 3 x 2 design with three levels of within subjects factor (repeated measures) and two levels to the between subjects factors.

I am interested in examining the changes from baseline and the interaction effect.

Question

• How do I compute the required sample size for a 3 x 2 design in order to achieve adequate statistical power?

Answer 1

• You need to decide what is acceptable statistical power for a given significance test. The rule of thumb of 80% power being reasonable is often bandied about. However, I think it is more sensible to see sample size selection as an optimisation problem, where statistical power is but one consideration, and the cost of collecting additional data is considered (see here for further discussion of my thoughts).
• Mixed ANOVA involves multiple potential significance tests. At the very least there are two main effects and an interaction. Potentially, there are also various comparisons. Each significance test can have different statistical power, and thus, literally, it does not make sense to speak of "the" statistical power of a mixed design as if it was a singular property. When determining the minimum sample size, you may want to think about which of the possible significance tests on the mixed ANOVA are important. If all of them are important, then you may want to consider the sample size required by the least powerful significance test.
• G Power 3 permits power analysis for all three types of significance tests in a mixed ANOVA (between subjects; within subjects; and interaction).
  • Download this free software and go to the tests - means - Repeated Measures ... menu.
  • The software permits a priori (i.e., calculate sample size for given effect size, alpha, power, and design) or post hoc (i.e., calculate power for given sample size, effect size, alpha, and design) power analysis.