The difference between family-wise error correction (FWE) and false discovery rate (FDR) reflects two different methodologies in handling the multiple testing problem (controlling type I error in the whole brain) of FMRI data analysis. AlphaSim and 3dClustSim belong to the FWE camp.

1) FWE: overall significance in the whole brain = P (≥ one false positive voxel in the whole brain)

- Frequentist’s perspective: Probability among many hypothetical brains
- Used usually for parametric testing

2) FDR = expected % false positive voxels among all "detected" voxels

- Focus: controlling false positives among detected voxels in one brain
- Can be used in parametric and non-parametric testing

3) Concrete example

- Suppose individual voxel p = 0.001 (uncorrected) for a brain of 25,000 EPI voxels
- With such an uncorrected p, on average we expect to have 25 false positive voxels in the whole brain
- In FWE sense: a corrected p = 0.05 means 5% false positives among MANY hypothetical brains for a FIXED voxel location
- In FDR sense: a corrected p = 0.05 indicates 5% voxels among those positively labeled voxels in THE brain are false positives

4) Which one to choose?

It is totally up to you! Since each method emphasizes one perspective in controlling type I error, they don't necessarily end up the same, and may differ dramatically sometimes because of each specific significance landscape in the brain and subtle issues in masking, for example. So in real practice choose whatever pleases you.

Hope this helps,
Gang