I am interested in estimating how many subjects should be included in a brain imaging study. Although the design is a fairly straight forward cross-sectional comparison, there are a number of tweakable image processing steps between the raw image and the processed image in which we carry out pixel-wise comparisons.
I've used the power.t.test function in R to estimate the number of subjects required to reach statistical significance, using hypothetical delta values and sd estimates from a control population. I've run these analyses with varying image processing settings, resulting in a large number of "number of subjects per group" vs "some image processing parameter" plots. So many that it looks kind of messy to provide hundreds of plots.
What I would like is an empirical equation that allows users to estimate the number of subjects per group as a function of effect size, alpha, and a few other image processing specific parameters. That way I only need to report the coefficients for the equation rather than supplying hundreds of graphs. Is this kind of thing possible?
So far if I model N ~ k1/effect.size^2 that looks OK for some values of alpha (for example) but doesn't work so good for others. A log-log plot doesn't model the relationship well either.
I can't seem to find an explicit formula that relates the number of subjects per group with the other factors in a power analysis. Does this exist?