  Distributions of Coulomb blockade peak spacing are reported for large
ensembles of both unbroken (magnetic field B = 0) and broken (B <> 0) time
reversal symmetry in GaAs quantum dots. Both distributions are symmetric and
roughly gaussian with a width ~ 2-6% of the average spacing, with broad,
non-gaussian tails. The distribution is systematically wider at B = 0 by a
factor of ~ 1.2 +- 0.1. No even-odd spacing correlations or bimodal structure
in the spacing distribution is found, suggesting an absence of spin-degeneracy.
There is no observed correlation between peak spacing and peak height.
