Gang,

Currently, I am not using 3dAnova, so I don't have a script to provide. However, I am considering using it in the future. My concerns about sphericity arise from the analysis of slow-related designs in which we include "time" (or "scan") as a factor. The levels of the time factor correspond to however many volumes are collected during a trial. For example, I may have a design in which I manipulate one within-subjects factor and then test for the interaction between that factor and the time factor, which would reveal brain regions for which my manipulated factor affects the shape of the hemodynamic response. Using the same design, I could also test for a main effect of the time factor, which would reveal brain regions for which any kind of reliable response occurs, regardless of the current condition. In both of these hypothetical analyses, sphericity is likely to be violated. This is somewhat related to the serial correlation issue, so perhaps 3dREMLfit would be relevant in this case, though my impression was that 3dREMLfit only came into play for regression analyses, and not the simple ANOVAs that I am talking about.

-Karin