How to describe study design looking at effect of a training program on two age groups  and how do I calculate required sample size? I am conducting an experiment on comparing the training effects on young and older adults (meaning it will be 2 independent groups). This also means it will be a repeated measure (within groups) because I will test the score before and after training. I think I should use mixed 2 way ANOVA. (Am I right?)
However I will also record the score before and after training in 2 different conditions. Is there a test to incorporate this variable as well?
And how would I estimate the sample size if I already have the mean and standard deviation from a similar study using that design?
Thank you in advance.
 A: I would recommend a mixed effects model, using the group assignment as the main fixed effect, and the person identity as the random effect (clustering on person). Format your data in the long format for this.
I'm not sure what you mean by "conditions", but this could also be incorporated as an indicator variable in your regression model.
I would recommend calculating sample size based on the expected contrast between the two groups based on their post-training score (and the SD associated with it, assuming you are measuring a continuous variable). You can ignore the baseline data for the sample size calculation.
You can use the sample size calculation tools at http://www.stat.uiowa.edu/~rlenth/Power/index.html, specifically the two-sample t test.
I hope this helps.
A: As already said by propofol, the question is what you mean by "condition"? If it is only another within-subjets factor (that is how I would read it) you could still use a mixed or split-plot ANOVA (instead of a mixed model).
You would have a 2 (between: young versus old) by 2 (within: before and after training), by 2 (within: condition A and B) design. In a design like this every individual would be tested four times (on both within factors 2 time; 2 * 2 = 4)
However, training effects would play a crucial role (i.e., which condition to start first, A or B) and you would have to think about something like a latin square design. It would probably be a lot better if condition would be another between-subjects factor if the skill aquired in each condition can spill over to the other and you are interested in genuine training effects.
For sample size estimation, gpower 3 is the correct program. It can cover such deisgns (I guess). However, you would have to specify which effect would be the one you are targeting at (in such a design it would necessarily be some kind of higher order interaction) but this seems odd in my opinion. Perhaps it is better to target on the training effect in the group with the smaller effect and try to get this one in a standard t-test (and estimate size for this effect). However, if you want the age-by-training interaction you would have to quantify that with the usual ANOVA effect sizes (e.g., eta-squared) or convert this into r-squared.
