The dependence of conductance fluctuations on parallel magnetic field is us
ed as a probe of spin degeneracy in open GaAs quantum dots. The variance of
fluctuations at high parallel field is reduced from the low-field variance
(with broken time-reversal symmetry) by factors ranging from roughly 2 in
a 1 mum(2) dot to greater than 4 in 8 mum(2) dots. The factor of 2 is expec
ted for Zeeman splitting of spin-degenerate channels. A possible explanatio
n for the larger suppression based on field-dependent spin-orbit scattering
is proposed.