Hi Shruti,

The beta weights of those regressors are estimated as follows by using the method of least square estimation (LSE):

vector of beta's = (X'X)^(-1) * X'Y

where X is the design matrix, and Y is the column vector of FMRI time series at one voxel. The meaning of the above estimation is this

(1) X'Y sums over the information from all the events for each condition type. For example, if there are n1 events of condition type A and n2 events of type B, then X'Y collects the information into a vector for types A and B plus the baseline.

(2) The information for each condition type is corrected by the overlap correction matrix X'X, which calibers each type based on the potential overlaps in the time course (i.e., set by lags in 3dDeconvolve).

These estimates are unabiased, sufficient, efficient, and consistent. The relevent property of the estimates to your question here is the consistency: A sequence of estimators is said to be consistent if it converges in probability to the true value of the parameter. In the case of regression analysis of 3dDeconvolve, the convergence rate is proportional to 1/n, where n is number of events.

Back to your case, the convergence rates for condition types A and B are in the order of 1/n1 and 1/n2 respectively. The activation tests for types A (whether beta1 = 0) and B (whether beta2 = 0), contrast tests (such as whether beta1 = beta2) are done by the following t statistics:

t = beta1/s(beta1) (type A)
t = beta2/s(beta2) (type B)

t =(beta1 - beta2)/[combination of s(beta1) and s(beta2)]

If n1 = 2*n2, the variance for estimate of beta1 is two times smaller than the one for that of beta2. If both n1 and n2 are small, this is a little concern. If both are big enough (such as 10 and 20), you should not worry about this since the imbalance is pretty marginal.

Other than the relative magnitude of n1 and n2, I suggest that you check the multicollearity of your design matrix with -nodata option before you implement the experiment.

Gang