  Using all the available empirical information, we analyze the spacing
distributions of low-lying 2-plus levels of even-even nuclei. To obtain
statistically relevant samples, the nuclei are grouped into classes defined by
the ratio R4/2 of the excitation energies of the first 4-plus and 2-plus
levels. This ratio serves as a measure of collectivity in nuclei. With the help
of Bayesian inference, we determine the chaoticity parameter for each class.
This parameter is found to vary strongly with R4/2 and takes particularly small
values in nuclei that have one of the dynamical symmetries of the interacting
Boson model.
