  We present the first application of statistical spectroscopy to study the
root-mean-square value of the parity nonconserving (PNC) interaction matrix
element M determined experimentally by scattering longitudinally polarized
neutrons from compound nuclei. Our effective PNC interaction consists of a
standard two-body meson-exchange piece and a doorway term to account for
spin-flip excitations. Strength functions are calculated using realistic
single-particle energies and a residual strong interaction adjusted to fit the
experimental density of states for the targets, ^{238} U for A\sim 230 and
^{104,105,106,108} Pd for A\sim 100. Using the standard Desplanques, Donoghue,
and Holstein estimates of the weak PNC meson-nucleon coupling constants, we
find that M is about a factor of 3 smaller than the experimental value for
^{238} U and about a factor of 1.7 smaller for Pd. The significance of this
result for refining the empirical determination of the weak coupling constants
is discussed.
