This page lists results of a few binning tests.

The b1 correlator is fairly easy to understand: binsizes from 1 to 7 give similar results, so the data is probably uncorrelated.

The Ds correlator is much messier: binsizes from 1 to 4 are similar, then binsizes from 6 to 9 are similar. Then the errorbars do strange things. I don't really understand what's happening here, unless it's possible that there are long-distance correlations without short-distance correlations. But that seems highly unlikely. Anyway, here's a plot:

Update:

We determined that blocksizes larger than 8 are statistically insignificant, and that the pi states are likely to be the most sensitive to binning. I've therefore done some tests to the pi data (local-local correlator only) with blocksizes ranging from 1 to 8. Here are the plots: