Hi Michael,

> 1)Why is session not considered a fixed effect?

Nobody had ever before asked for the option of fixed effects in the model. I can add such an option soon.

> Does 3dICC_REML only include the (2, 1) ICC model and not the (3, 1) ICC model?

The ICC computation is an extension of the traditional methods such as ICC(2,1) and ICC(3,1). See more discussion in Chen, G., Saad, Z.S., Britton, J.C., Pine, D.S., Cox, R.W. (2013). Linear Mixed-Effects Modeling Approach to FMRI Group Analysis.
NeuroImage 73:176-190.

> 2) Do the results reflect consistency or absolute agreement? Is there an option for either one?

I'm not so sure abou the difference between the two. The interpretation I'm familiar with is discussed in the manual webiste [afni.nimh.nih.gov]

> 3) For each factor, there is a correlation coefficient, but no corresponding p-value?
> Is there a round about way to calculate the appropriate p-value?

I've never seen a way to associate the ICC with a p-value. Do you happen to know any literature about this?

> 4) If i wanted to run separate 3dICC_REML's for two groups. How would I compare the results
> from both groups (i.e., Comparing ICC correlation coefficients between groups)?

What else are you looking for?

> 5) We have 3 sessions, a .75 value for session indicates that 75% of the variability
> is accounted for across 3 sessions. Which would seem like a good indicator of reliability.
> If there were differences among the 3 sessions, then the icc value would be low, correct?

Some misunderstanding here. The ICC value is a relative measure in the sense that it's relative to the other variables you incorporated in the model. So a ICC value of 0.75 for session means that, among all variables, session accounts for 75% of total variability while 25% comes from other sources (e.g., subjects). So if the differences among the 3 sessions were big, the ICC for session would be high.

Gang