Hi folks,
Assume a factorial design with two factors with 2 and 4 levels. It was originally designed as a 2x4 factorial trials with interests in two main effects and interactions. This is clear to me - a simple design would be a 2x4 factorial design, and the sample size was based on performing a two-way ANOVA based on pre-specified effect size.
Now, the main interests changed a bit to the main effects and a few pre-specified individual contrasts within the 4 level factor (not all pairwise comparisons). Of course, I now need to power my study based on these contrast (multiple calculations based on t-test with pre-specified effect sizes between levels). The final sample size may be significantly increased.
I would like to ask if this is how people who approach the planning of this kind of study. I am not sure if the interest becomes the individual contrasts, would a factorial design still be ideal?
If you were only interested in 2 or 3 contrasts then a factorial design might be an overkill. It’s probably still appropriate for you. If you had data from a previous study it would be easy to get all the interesting contrasts simultaneously (with a built-in optimal multiplicity correction) from which you could solve for the needed sample size to yield a sufficiently better margin of error (half-width of contrast confidence intervals). More traditional planning might be based on the power of the least powerful contrast, using t-test-like ideas but with larger error d.f.