  We study the energy level statistics of the states in U(5) and O(6) dynamical
symmetries of the interacting boson model and the high spin states with
backbending in U(5) symmetry. In the calculations, the degeneracy resulting
from the additional quantum number is eliminated manually. The calculated
results indicate that the finite boson number $N$ effect is prominent. When $N$
has a value close to a realistic one, increasing the interaction strength of
subgroup O(5) makes the statistics vary from Poisson-type to GOE-type and
further recover to Poisson-type. However, in the case of $N \to \infty$, they
all tend to be Poisson-type. The fluctuation property of the energy levels with
backbending in high spin states in U(5) symmetry involves a signal of shape
phase transition between spherical vibration and axial rotation.
