I'm troubling over the role of number of observations in a within subjects design on power. Let's say I have a 2x2, or even a single factor, completely within subjects design. A power analysis might tell me I need a relatively small sample, say <50 (depending on the size of effect I'm looking for, etc.). However, what if I only have 10 trials, versus 100 trials? How do I add that as a parameter? Surely the number of observations per participant will impact the stability of my results.
Now, let's say I have a large number of observations per participant; each participant receives 100 trials, 50 in each condition. But what if I only care about a small number of trials - for example, items rated as "very confident" on a memory task? I may obtain very few (and potentially 0) trials per participant with the response I'm interested in examining. How do I plan for this, and what should this mean if I'm trying to figure out my appropriate sample size?