  We study the finite-volume effects in our calculation of $B_K$ using
HYP-smeared improved staggered valence fermions. We calculate the predictions
of both SU(3) and SU(2) staggered chiral perturbation theory at one-loop order.
We compare these to the results of a direct calculation, using MILC coarse
lattices with two different volumes: $20^3$ and $28^3$. From the direct
calculation, we find that the finite volume effect is $\approx 2%$ for the
SU(3) analysis and $\approx 0.9%$ for the SU(2) analysis. We also show how the
statistical error depends on the number of measurements made per configuration,
and make a first study of autocorrelations.
