Q What is a state imbalance?

A SAMsrc computes the value

where a and c vary over the N voxels of the active and control images, respectively. This value should be close to zero. If it is not, it means that either the active or the control state has excess power.

One way this can happen is if your active and control windows are of unequal length. Covariance is a normalized quantity, meaning it doesn't depend directly on the sample size; however there is still the question of convergence. Brain signals are highly non-stationary, and you may need a lot of data (but not too much!) in order to get a good estimate of the covariance.

Because of the potentially slow convergence of the covariance, the estimated power at each voxel is somewhat greater for a covariance matrix generated from a greater number of samples (longer window, or more windows). Thus, there will be a bias in a dual-state image.

In general, you don't need to have exactly the same number of samples for active and control, but you will see this bias if your window sizes are too different. Using 3dNormalize with -z is an option to remove the bias if you have reason to believe that simply shifting the distribution to zero will work. (Check the shape of the distribution using 3dhistog, it should be roughly normal.)

State imbalances can also occur if there are large noise events generating excess power in some of the windows. To solve this problem you need to clean the data by deleting the marks near the bad spots.

Another possible cause of state imbalances, especially in low-frequency bands such as delta (1–3 Hz) or theta (4–8 Hz), are artifacts such as eye-blinks, motion, or metal contamination which can introduce linear dependencies in the covariance, and which might be difficult to clean. In this case, regularization can help (-u option to SAMsrc).