We present the first application of statistical spectroscopy to study the r
oot-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
0 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, U-238 for A similar to
230 and Pd-104,Pd-105,Pd-106,Pd-108 for A similar to 100. Using the standar
d Desplanques-Donoghue-Holstein estimates of the weak PNC meson-nucleon cou
pling constants, we find that M is about a factor of 3 smaller than the exp
erimental value for U-238 and about a factor of 1.7 smaller for Pd. The sig
nificance of this result for refining the empirical determination of the we
ak-coupling constants is discussed.