# Group analysis questions about random effect model in 3dANOVA2

I am a beginner in AFNI group analysis and I have the following problem when looking at and comparing commands such as 3dANOVA, 3dANOVA2 or 3dANOVA3:

1. In the help file of 3dANOVA2, random fators are mentioned in options -type 2 and -type 3. I would like to know how ''random'' is defined here. In the Examples of 3dANOVA2, a one-way within-subject ANOVA was actually conducted, as each subject tried three types of DONUTS. But in this example, the SUBJECT is treated as a random factor. When I have analyzed behavioral data in other statistical analysis software before, I remember never thinking of a SUBJECT as a random factor. Can anyone explain why AFNI treats SUBJECT as a random factor when processing brain data?

2. A design similar to the previous problem appears in the 3dANOVA example: The 3dANOVA help file gives an example in which two subjects (fred and ethel) both viewed three types of stimuli (faces, houses, an donuts). It is obviously also a one-way within-subject design, but its ANOVA analysis uses the 3dANOVA command and does not involve treating SUBJECT as a random factor. This confuses me a lot, and according to what I have known, one-way within-subject ANOVA should be done using 3dANOVA2. Can someone help me explain this?

3. Going back to the use of 3dANOVA2, I would like to find an example of experimental design using -type 2, i.e., a random effects model (A and B are both random factors). My previous understanding of random factor is that such an influencing factor cannot be artificially manipulated to traverse all possibilities. For example, when investigating the influence of fertilization amount on crop yield, rainfall is a random factor. I don't know if my understanding is accurate or comprehensive enough, I hope someone can give me an example of using the -type 2 option and both factors are random.

`3dANOVA2 -type 3` would be used for a conventional one-way within-subject (or repeated-measures) ANOVA. If you find the concept of a "random factor" confusing, consider using `3dMVM` , which is a generic program for all types of ANOVA / ANCOVA.