Hello Yufeng:

Yes, as the statistics textbooks say, the statistical power depends on the
sample size. However, fMRI experiments differ from "conventional" experiments
in that the measurements are not absolute, but are relative. Relative to the
baseline, or relative to each other. Roughly speaking, for fMRI experiments,
most of the information comes from transitions between mental states, rather
than repeated measurements of a constant state.

Let us assume that the length (number of TR's) of the experiment is fixed.
One must decide how many trials to place within the limited time available.
For "conventional" type experiments, the more trials the better. However, in
fMRI experiments, too many trials is just as bad as too few trials.

One way to evaluate different hypothetical experimental designs is to use
the "-nodata" option of 3dDeconvolve (which is described in Sections 1.4.1 and
3.4 of the documentation in file 3dDeconvolve.ps). Determination of the
optimal experimental design depends, in part, on the choice of the parameter(s)
of interest. For example, if you are interested in the difference between
the AUC for two stimuli, you can set up the GLT for this difference. Then,
using the -nodata option, 3dDeconvolve will calculate the "norm. std. dev."
for the corresponding LC[0] coefficient. Since the t-stat for the LC[0]
coefficient (i.e., t-stat for difference in AUC's) is inversely proportional
to the std. dev. of that parameter, the optimal experimental design is chosen
by minimizing the "norm. std. dev.".

In general, the minimum of the "norm. std. dev." curve is rather flat. And,
of course, there are other objectives and considerations in selecting the
experimental design. I'm just suggesting that this should be one of the
considerations, and this approach should help avoid really bad experimental
designs (e.g., multicollinearity). It's always a good idea to evaluate the
experimental design before conducting the experiment.

Finally, a number of assumptions are involved in the above evaluation of
alternative experimental designs. For an in-depth study of parameter estimation
accuracy, statistical significance, and statistical power, there is the
alternative approach of Monte Carlo simulation. For (a few) more details,
please see Chapter 4 of 3dDeconvolve.ps.

Doug Ward